52mm
Financial Management
N i n t h
E d i t i o n
Ninth
Edition
Now in its 9th edition, Financial Management is the leading text on the theory and application of corporate finance in southern
Africa. Set against the backdrop of recent developments in financial markets, instruments and financial theory, the text refers to
real-world applications and financial decisions by South African companies.
The book includes chapters on:  the time value of money  risk and return  portfolio management  financial statement
analysis  bond and equity valuations  the cost of capital  capital budgeting  working capital management  sources of
finance  capital structure  leasing  dividends and share buybacks  mergers, acquisitions and corporate restructuring 
risk management and derivatives  international finance  business planning and financial modelling  corporate strategy and
business models.
New features
•
behavioural finance and how biases can impact on corporate financial decision making
•
sections on market efficiency, market anomalies, ETFs and investor behaviour
•
meets the requirements of Version 10 of SAICA’s Competency Framework, effective from January 2019, in respect to
financial management, financial risk management and corporate strategy
•
incorporates the latest developments that affect corporate finance: King IV; tax legislation; the Companies Act; rules of
the JSE and capital markets; International Financial Reporting Standards (IFRS); official guidelines on corporate valuations
and integrated reporting, business rescue, rules on mergers and acquisitions and competition law
•
expanded sections on the use and drawbacks of IRR and Excel® functions such as XNPV and XIRR
•
sections on Value at Risk (VaR), Monte Carlo simulation in Excel® and expanded chapter on derivatives
•
expanded sections on forecasting and the market and income approaches to valuation
•
new section on retirement planning, living annuities and pensions
•
sections on smart contracts, distributed ledger systems (blockchain) and business disruption
•
expanded sections on CAPM and multi-factor models
•
new sections on leases and the impact of IFRS16 (effective from 2019) on equity valuations, the cost of capital, financial ratios and capital structure
•
new section on the resource-based view of the firm and how this aligns with integrated reporting
•
expanded guidance sections at the end of key chapters to assist readers to better understand and integrate key areas
in finance
•
inclusion of recent ITC questions and solutions.
Support material
Support material is made available to all prescribing institutions. It includes:  answers to all chapter questions  PowerPoint®
slides  multiple choice question tests and solutions  selected readings  videos and Excel® models.
This book is recommended for  undergraduate and postgraduate commerce or business students  ITC and APC candidates
 practising accountants  internal and independent auditors  business managers, corporate finance practitioners, strategists
and analysts.
Carlos Correia
Other features
•
professional ethics and codes of conduct updated in terms of revisions by SAICA and CFA
•
use of Excel® models to provide detailed explanations of each topic in finance
•
extensive number of questions provided per chapter
•
relevant examples used to demonstrate application of finance theory
•
reference to insights and views of Warren Buffett on finance theory.
Financial
Management
N i n t h
E d i t i o n
Carlos Correia
www.juta.co.za
9TH EDITION
financial
management
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9TH EDITION
financial
management
Carlos Correia
Founding authors:
Carlos Correia, David Flynn, Enrico Uliana,
Michael Wormald
Main contributor:
Johnathan Dillon
Contributors:
Obeid Mahomed
Darron West
Ameer Amod
Gizelle Willows
Joel Stern
Glen Holman
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Zwelakhe Mnguni
Greg Beech
Gary Swartz
Kwasi Okyere-Boakye
Etienne Swanepoel
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Financial Management
First published in 1987
Second edition 1988
Third edition 1993
Fourth edition 2000
Reprinted 2001, 2002
Fifth edition 2003
Reprinted 2003 (twice), 2005
Sixth edition 2007
Reprinted 2007, 2008, 2010 (twice)
Seventh edition 2011
Reprint 2012
Eighth edition 2015
Reprinted 2015, 2016, 2017, 2018
Ninth edition 2019
Juta and Company (Pty) Ltd
First floor, Sunclare building, 21 Dreyer street, Claremont 7708
PO Box 14373, Lansdowne 7779, Cape Town, South Africa
www.juta.co.za
© 2019 Juta and Company (Pty) Ltd
ISBN 978 1 48512 957 8 (Print)
ISBN 978 1 48512 958 5 (WebPDF)
All rights reserved. No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopying, recording, or
any information storage or retrieval system, without prior permission in writing from
the publisher. Subject to any applicable licensing terms and conditions in the case of
electronically supplied publications, a person may engage in fair dealing with a copy of this
publication for his or her personal or private use, or his or her research or private study.
See section 12(1)(a) of the Copyright Act 98 of 1978.
Project manager: Carlyn Bartlett-Cronje
Proofreaders: Helen Correia, Edith Viljoen, Tarryn Witten and Ross Compton
Cover designer: Jacques Nel
Typesetter: Wouter Reinders
Indexer: Clifford Perusset
Typeset in 10 pt on 12 pt Dutch BT
The author and the publisher believe on the strength of due diligence exercised that
this work does not contain any material that is the subject of copyright held by another
person. In the alternative, they believe that any protected pre-existing material that
may be comprised in it has been used with appropriate authority or has been used in
circumstances that make such use permissible under the law.
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Contents
– a concise overview
Chapter 1
Overview of financial management . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
Chapter 2
The time value of money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
Chapter 3
Risk and return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
Chapter 4
Portfolio management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
Chapter 5
Financial statement analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
Chapter 6
Valuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
Chapter 7
The cost of capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1
Chapter 8
Capital budgeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1
Chapter 9
Further issues in capital budgeting . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1
Chapter 10
Capital budgeting: Risk analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1
Chapter 11
Working capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1
Chapter 12
Current asset management and short-term financing . . . . . . . . . . . 12-1
Chapter 13
Sources of finance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1
Chapter 14
Capital structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1
Chapter 15
Leasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1
Chapter 16
Dividends and share buy-backs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1
Chapter 17
Mergers, acquisitions and corporate restructuring . . . . . . . . . . . . . 17-1
Chapter 18
Risk management and derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1
Chapter 19
International financial management . . . . . . . . . . . . . . . . . . . . . . . . . 19-1
Chapter 20
Business planning and financial modelling . . . . . . . . . . . . . . . . . . . 20-1
Chapter 21
Corporate strategy and business models . . . . . . . . . . . . . . . . . . . . . 21-1
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T-2
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1
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Contents
Preface...........................................................................................................................................xxv
What does the book offer?.........................................................................................................xxvi
What resources does the book offer to the instructor?............................................................xxix
How does the book fit in with SAICA’s Competency Framework for Financial
Management?..............................................................................................................................xxxi
Chapter 1 Overview of financial management...........................................................................1-1
Learning objectives.......................................................................................................................1-1
Introduction..................................................................................................................................1-1
1 The context of financial management...................................................................................1-2
Development of financial management................................................................................1-2
Links with economics..............................................................................................................1-2
Links with accounting.............................................................................................................1-2
2 The environment of financial management..........................................................................1-3
Forms of business organisations............................................................................................1-6
Taxation....................................................................................................................................1-8
Taxation of company profits...................................................................................................1-9
Capital gains tax......................................................................................................................1-9
Dividend withholding tax.......................................................................................................1-9
3 What is the fundamental objective of financial management?.........................................1-10
Why is profit maximisation not the right objective for corporate finance?.....................1-10
Manipulation of accounting profits.....................................................................................1-10
Accounting profits and the cost of capital..........................................................................1-11
Risk........................................................................................................................................1-11
Shareholders want management to maximise value...........................................................1-11
Focus of financial management on decision-making.........................................................1-11
Economic Value Added (EVA)............................................................................................1-12
What about the ethics of maximising value?......................................................................1-13
4 The role of the financial manager.......................................................................................1-14
Opportunities to create wealth............................................................................................1-14
Investment in operating assets.............................................................................................1-14
Investment in financial assets...............................................................................................1-15
Selecting the optimal finance mix........................................................................................1-15
Finance from capital markets..............................................................................................1-16
The interaction of investment and financing decisions......................................................1-17
From the real world: BHP, Shoprite, Truworths,Vodacom and Pioneer Foods...............1-20
5 Fundamental concepts of corporate finance......................................................................1-21
Present Value.........................................................................................................................1-21
Time value of money............................................................................................................1-21
Risk and return.....................................................................................................................1-21
No Arbitrage Principle.........................................................................................................1-21
Efficient markets...................................................................................................................1-22
Portfolio theory.....................................................................................................................1-23
Capital asset pricing model..................................................................................................1-23
Financial analysis..................................................................................................................1-23
6 Do managers act in the interest of shareholders?.............................................................1-23
Management incentives, share options and the financial crisis.........................................1-25
Another agency problem: shareholders and bondholders.................................................1-26
7 Doing the right thing: ethics in business and King IV......................................................1-27
8 Corporate Governance and King IV....................................................................................1-27
The King IV Code................................................................................................................1-28
What is the board’s primary governance role and responsibilities?.................................1-29
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King IV Principles.................................................................................................................1-30
The audit committee.............................................................................................................1-32
Directors and the separation of the CEO and the chairperson functions........................1-32
Sustainability and integrated reporting...............................................................................1-32
Risk management..................................................................................................................1-32
Information Technology (IT) and its role in corporate finance........................................1-33
Solvency and liquidity tests..................................................................................................1-33
Business rescue......................................................................................................................1-33
Does corporate governance pay?.........................................................................................1-33
Auditors.................................................................................................................................1-34
From the real world … application of King IV by Netcare...............................................1-35
What does Charlie Munger think about corporate governance?......................................1-35
Case study: Tiger Brands and society..................................................................................1-36
9 Corporate Strategy...............................................................................................................1-37
Porter’s Five Forces Model..................................................................................................1-37
Rivalry among existing firms................................................................................................1-37
Threat of substitute products...............................................................................................1-38
Threat of new entrants and barriers to entry......................................................................1-39
Bargaining power of buyers..................................................................................................1-40
Bargaining power of suppliers.............................................................................................1-40
Competitive strategies: cost leadership and differentiation..............................................1-41
SWOT analysis......................................................................................................................1-41
PESTEL analysis...................................................................................................................1-43
Sustainability related issues..................................................................................................1-44
10 Behavioural Finance.............................................................................................................1-45
11 Structure of the text..............................................................................................................1-45
Summary................................................................................................................................1-45
Appendix 1.1 An introduction to behavioural finance.......................................................1-46
Appendix 1.2 Professional ethics and codes of conduct....................................................1-52
Appendix 1.3 Stakeholder considerations and good corporate citizenship......................1-55
Questions...............................................................................................................................1-59
Chapter 2 The time value of money............................................................................................2-1
Is compound interest ‘the most powerful force in the universe’?.............................................2-1
Learning objectives.......................................................................................................................2-1
Introduction..................................................................................................................................2-1
1 Future value............................................................................................................................2-2
Single amount, single period..................................................................................................2-2
Single amount, multiple periods, annual interest compounded..........................................2-2
Single amount, multiple periods, non-annual compounding...............................................2-7
Annual effective rate..............................................................................................................2-8
Continuous compounding......................................................................................................2-9
Interpolation............................................................................................................................2-9
Series of investments, ordinary annuity (FVA) – multiple investments and multiple
periods...................................................................................................................................2-10
Series of investments, annuity due......................................................................................2-12
Future values when the timing of the cash flows and the compounding periods differ.....2-13
2 Present values.......................................................................................................................2-13
Single amount, single period, annual discounting..............................................................2-14
Single amount, multiple periods, annual discounting........................................................2-14
Stream of cash flows, ordinary annuity (PVA)...................................................................2-15
Stream of cash flows, annuity due.......................................................................................2-16
Stream of cash flows, deferred annuity...............................................................................2-18
Uneven stream of cash flows................................................................................................2-19
Perpetuities............................................................................................................................2-20
Growing perpetuities............................................................................................................2-20
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3
4
5
6
Growing annuity....................................................................................................................2-21
Inflation and real returns.....................................................................................................2-21
Some real-world applications..............................................................................................2-22
Retirement planning.............................................................................................................2-22
Loan amortisation schedules................................................................................................2-23
Mortgage loan.......................................................................................................................2-24
Financial calculators and spreadsheets..............................................................................2-25
Using financial calculators...................................................................................................2-25
Using Excel spreadsheets.....................................................................................................2-27
The role of interest rates......................................................................................................2-30
The expectations theory.......................................................................................................2-32
The liquidity preference theory...........................................................................................2-32
The market segmentation theory.........................................................................................2-33
Applying the time value of money principles to bonds......................................................2-33
Perpetuals and 100-year bonds............................................................................................2-36
Summary................................................................................................................................2-38
Self-study problems...............................................................................................................2-39
Solutions to self-study problems..........................................................................................2-40
Appendix 2.1: Retirement planning: living annuities, the 4% rule and the looming
pension crisis.........................................................................................................................2-43
Questions...............................................................................................................................2-54
Chapter 3 Risk and return..........................................................................................................3-1
The 21st Century: a time of financial crisis and recovery for equities.....................................3-1
Learning objectives.......................................................................................................................3-1
Introduction..................................................................................................................................3-2
1 The concept of risk.................................................................................................................3-3
Business risk............................................................................................................................3-3
Financial risk...........................................................................................................................3-7
Total company risk..................................................................................................................3-8
2 Measuring expected return and risk.....................................................................................3-9
Measuring the expected return on a single share.................................................................3-9
Measuring risk for a single share.........................................................................................3-10
The mean–variance rule.......................................................................................................3-11
3 Interpreting the summary statistics....................................................................................3-12
Properties of a normal distribution.....................................................................................3-12
Comparison of single shares................................................................................................3-14
Co-efficient of variation.......................................................................................................3-15
The z score.............................................................................................................................3-16
Co-variance and correlation.................................................................................................3-18
Value at Risk (VaR)..............................................................................................................3-19
Expected Shortfall.................................................................................................................3-20
Historical returns..................................................................................................................3-21
4 Risk and return in financial markets.................................................................................3-23
Emerging markets.................................................................................................................3-30
Volatility and time periods: the Rip van Winkle solution to risk......................................3-31
What does Warren Buffett think?........................................................................................3-31
Risk-adjusted measures of performance.............................................................................3-32
From the real world: Unit trust funds.................................................................................3-33
What returns did Warren Buffett achieve with Berkshire Hathaway?.............................3-34
Summary................................................................................................................................3-35
Appendix 3.1 A behavioural finance perspective on risk and return................................3-36
Appendix 3.2 Compound annual returns, arithmetic averages and total shareholder
returns....................................................................................................................................3-39
Self-study problems...............................................................................................................3-42
Suggested solutions...............................................................................................................3-43
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Questions...............................................................................................................................3-44
Chapter 4 Portfolio management................................................................................................4-1
Diversify to reduce risk................................................................................................................4-1
Learning objectives.......................................................................................................................4-1
Introduction..................................................................................................................................4-2
1 Two-asset portfolio risk and return......................................................................................4-2
Measuring two-asset portfolio returns..................................................................................4-2
The principles of portfolio risk..............................................................................................4-3
Measuring two-asset portfolio risk........................................................................................4-7
Positioning an investor on the efficient frontier.................................................................4-12
2 Multiple-share portfolio risk and return............................................................................4-13
The benefits of diversification.............................................................................................4-15
Introducing a risk-free asset.................................................................................................4-16
3 Beta analysis.........................................................................................................................4-18
Beta as a measure of portfolio risk......................................................................................4-19
Beta and the capital asset pricing model (CAPM).............................................................4-21
4 The efficient markets hypothesis.........................................................................................4-24
The weak form......................................................................................................................4-24
The semi-strong form...........................................................................................................4-25
The strong form....................................................................................................................4-25
Market efficiency: the evidence...........................................................................................4-25
Evidence of the efficiency of the JSE..................................................................................4-26
Is the CAPM used in practice?............................................................................................4-27
5 Exchange traded funds (ETFs) and unit trusts.................................................................4-28
From the real world..............................................................................................................4-30
Summary................................................................................................................................4-30
Guidance to portfolio management: the risk and return concepts linking Chapters 3
and 4.......................................................................................................................................4-31
Self-study problem................................................................................................................4-33
Suggested solution................................................................................................................4-34
Appendix 4.1 Calculating the beta co-efficient..................................................................4-35
Appendix 4.2 Perspectives: Estimating the beta co-efficient.............................................4-39
Appendix 4.3 Perspectives: Behavioural finance................................................................4-44
Appendix 4.4 Investment decision-making under conditions of uncertainty...................4-46
Appendix 4.5 Prospect theory..............................................................................................4-48
Questions...............................................................................................................................4-49
Chapter 5 Financial statement analysis.....................................................................................5-1
Companies and investors employ financial ratios to evaluate performance............................5-1
Learning objectives.......................................................................................................................5-1
Introduction..................................................................................................................................5-2
1 Annual financial statements and the Integrated Report.....................................................5-2
Integrated Report...................................................................................................................5-2
From the real world: Truworths’ Integrated Report............................................................5-5
Annual Financial Statements.................................................................................................5-5
Statement of Comprehensive Income (Statement of Profit or Loss and
Other Comprehensive Income).............................................................................................5-7
Statement of Financial Position.............................................................................................5-8
Statement of Cash Flows........................................................................................................5-8
2 Objectives of financial analysis and stakeholders...............................................................5-9
Shareholders............................................................................................................................5-9
Credit grantors........................................................................................................................5-9
Management..........................................................................................................................5-10
Employees..............................................................................................................................5-10
Customers..............................................................................................................................5-10
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3
4
5
6
7
8
9
10
Suppliers................................................................................................................................5-11
Acquisition and merger analysts..........................................................................................5-11
Auditors.................................................................................................................................5-11
Government...........................................................................................................................5-11
Limitations of accounting data............................................................................................5-11
Monetary expression.............................................................................................................5-11
Simplification and summarisation.......................................................................................5-12
Flexible accounting policies.................................................................................................5-12
Inflation.................................................................................................................................5-12
Approaches to financial statement analysis.......................................................................5-12
Comparative financial statements........................................................................................5-12
Index analysis........................................................................................................................5-13
Common size analysis...........................................................................................................5-14
Ratio analysis.........................................................................................................................5-15
Application of ratio analysis................................................................................................5-15
Liquidity ratios......................................................................................................................5-15
Asset management ratios.....................................................................................................5-16
Debt management ratios......................................................................................................5-19
Profitability ratios.................................................................................................................5-21
Cash flow ratios.....................................................................................................................5-24
Market value ratios...............................................................................................................5-25
Structured ratio analysis......................................................................................................5-26
Du Pont analysis....................................................................................................................5-26
Failure prediction.................................................................................................................5-28
Financial distress models......................................................................................................5-28
Limitations of ratio analysis................................................................................................5-29
Economic Value Added (EVA™)..........................................................................................5-30
The use of EVA to measure performance..........................................................................5-32
Perspectives on EVA™ by Joel Stern..................................................................................5-33
What’s behind the numbers?...............................................................................................5-34
Understand the business and the industry sector...............................................................5-34
Understand management’s motives for selecting accounting policies..............................5-34
Understand the key drivers of value....................................................................................5-35
Understand which accounting policies are flexible............................................................5-35
Accounting for leases............................................................................................................5-35
Understand the warning signs..............................................................................................5-36
Understand the business and financial risks facing the company.....................................5-38
Sensitivity analysis.................................................................................................................5-38
Further factors to consider when analysing a company.....................................................5-38
From the real world..............................................................................................................5-41
Summary................................................................................................................................5-42
Guidance on Financial Analysis..........................................................................................5-43
Self-study problems...............................................................................................................5-45
Solutions to self-study problems..........................................................................................5-47
Appendix 5.1 Sustainable growth........................................................................................5-48
Appendix 5.2 The three most crucial ratios in equity analysis..........................................5-51
Appendix 5.3 Truworths and the outcomes of the six capitals..........................................5-55
Questions...............................................................................................................................5-56
Chapter 6 Valuations...................................................................................................................6-1
Pricing on the JSE and value: Why Edcon used valuation principles to go private................6-1
Learning objectives.......................................................................................................................6-1
Introduction..................................................................................................................................6-1
1 Valuation – an overview.........................................................................................................6-2
What are the fundamental building blocks of a valuation?.................................................6-2
2 The effect of risk and return on valuations..........................................................................6-3
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3 Required rate of return..........................................................................................................6-3
4 Valuation of debentures and bonds.......................................................................................6-4
Debentures and bonds in perpetuity.....................................................................................6-4
Redeemable debentures and bonds.......................................................................................6-5
From the real world … Valuation of Eskom bonds..............................................................6-7
5 Valuation of preference shares..............................................................................................6-8
Cumulative non-redeemable preference shares...................................................................6-9
Non-cumulative preference shares......................................................................................6-10
Redeemable preference shares............................................................................................6-10
6 Valuation of ordinary equity................................................................................................6-10
Dividend discount model......................................................................................................6-11
Constant growth in dividends...............................................................................................6-11
Limitations.............................................................................................................................6-14
Zero growth in dividends.....................................................................................................6-14
Valuing shares with a non-constant growth rate.................................................................6-15
Valuing shares which do not pay dividends for many years...............................................6-17
From the real world: Woolworths........................................................................................6-17
Price multiples (relative valuation).....................................................................................6-18
The price-earnings (P/E) ratio.............................................................................................6-18
Using EBITDA or EBIT multiples to determine enterprise value...................................6-21
Market to book ratio............................................................................................................6-22
Price to sales ratio.................................................................................................................6-23
Free cash flow model (discounted cash flow model).........................................................6-23
Terminal values......................................................................................................................6-24
The Economic Value Added (EVATM) approach................................................................6-26
Valuation of rights.................................................................................................................6-28
The impact of share options on equity valuations..............................................................6-28
Leases and valuations...........................................................................................................6-29
7 Valuations and the financial manager................................................................................6-30
Pitfalls....................................................................................................................................6-30
Challenges.............................................................................................................................6-31
Perspectives: Valuations in the real world..........................................................................6-31
Summary................................................................................................................................6-33
Self-study problems...............................................................................................................6-33
Solutions to self-study problems..........................................................................................6-34
Appendix 6.1 Lack of marketability discount and other adjustments..............................6-37
Appendix 6.2 Exploring selected issues in valuations........................................................6-39
Appendix 6.3 Perspectives: The subjective nature of valuations.......................................6-42
Questions...............................................................................................................................6-43
Chapter 7 The cost of capital......................................................................................................7-1
The weighted-average cost of capital of Sasol...........................................................................7-1
Learning objectives.......................................................................................................................7-1
Introduction..................................................................................................................................7-1
1 The weighted-average cost of capital....................................................................................7-2
2 The weighted-average cost of capital – principles and formula.........................................7-3
3 The pooling of funds approach..............................................................................................7-4
4 Component costs of capital....................................................................................................7-6
Cost of new debt (Kd).............................................................................................................7-8
The cost of debt and Section 24J of the Income Tax Act....................................................7-9
Cost of preference shares (Kp).............................................................................................7-11
Cost of shareholders’ equity.................................................................................................7-12
Dividend yield and growth method.....................................................................................7-13
Capital asset pricing model (CAPM)..................................................................................7-14
Bond yield plus a risk premium method.............................................................................7-14
5 Weighting components of capital structure........................................................................7-15
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6
7
8
9
10
11
Calculating the WACC.........................................................................................................7-17
Breaks in the WACC.............................................................................................................7-18
Funds from the non-cash flow items...................................................................................7-19
Estimating the cost of capital of divisions..........................................................................7-19
Operating leases, capital structure and the weighted-average cost of capital................7-21
The weighted-average cost of capital – some practical issues..........................................7-22
The risk-free rate..................................................................................................................7-22
The market (equity) risk premium......................................................................................7-23
Surveys...................................................................................................................................7-24
Using the dividend growth model to determine the market risk premium......................7-24
Other indicators of the market risk premium.....................................................................7-25
Warren Buffett’s view...........................................................................................................7-25
Betas.......................................................................................................................................7-25
Adjustments to the cost of equity and WACC....................................................................7-26
The financial crisis, emerging markets and the cost of capital..........................................7-26
Taxation..................................................................................................................................7-28
The role of hurdle rates........................................................................................................7-28
From the real world: The cost of capital of South African firms......................................7-28
Summary................................................................................................................................7-31
Guidance on cost of capital..................................................................................................7-31
Appendix 7.1 CAPM and the Fama-French Three-Factor Model....................................7-33
Does CAPM work?...............................................................................................................7-33
Fama-French Three-Factor Model......................................................................................7-34
Other factor models..............................................................................................................7-35
Appendix 7.2 The Downside CAPM: A robust alternate to the CAPM?........................7-36
Self-study problems...............................................................................................................7-38
Solutions to self-study problems..........................................................................................7-40
Questions...............................................................................................................................7-43
Chapter 8 Capital budgeting.......................................................................................................8-1
Expanding horizons: Kumba scales up production to meet demand for iron ore...................8-1
Learning objectives.......................................................................................................................8-1
Introduction..................................................................................................................................8-1
1 Types of investment projects..................................................................................................8-2
Replacement or expansion.....................................................................................................8-2
Independent and mutually exclusive projects.......................................................................8-3
Divisible and indivisible projects...........................................................................................8-3
2 Capital budgeting techniques................................................................................................8-3
Net present value (NPV)........................................................................................................8-4
The internal rate of return (IRR).........................................................................................8-5
Payback method......................................................................................................................8-8
Accounting rate of return.......................................................................................................8-9
Discounted payback..............................................................................................................8-11
The profitability index..........................................................................................................8-11
Modified internal rate of return..........................................................................................8-12
Economic Value Added (EVA™) or economic profit........................................................8-12
3 Cash flow determination......................................................................................................8-14
Beginning-of-project cash flows...........................................................................................8-15
Annual operating cash flows................................................................................................8-15
Cash flow determination – some rules................................................................................8-16
Taxation..................................................................................................................................8-19
Depreciation allowances.......................................................................................................8-19
Recoupments and scrapping allowances.............................................................................8-21
Taxation effects of replacement decisions...........................................................................8-23
Capital Gains Tax..................................................................................................................8-23
End-of-project cash flows.....................................................................................................8-24
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Application............................................................................................................................8-25
4 Post-audits.............................................................................................................................8-27
Summary................................................................................................................................8-28
Self-study problems...............................................................................................................8-29
Solutions to self-study problems..........................................................................................8-30
Guidance on capital budgeting............................................................................................8-32
Appendix 8.1 NPV/IRR: Conflict in rankings....................................................................8-34
Questions...............................................................................................................................8-36
Chapter 9 Further issues in capital budgeting..........................................................................9-1
It is Ayoba time! Connecting Africa and the Middle East........................................................9-1
Learning objectives.......................................................................................................................9-1
Introduction..................................................................................................................................9-1
1 Comparing projects with unequal lives................................................................................9-2
Unequal lives and project evaluation....................................................................................9-2
Replacement chains................................................................................................................9-4
Equivalent annual annuities...................................................................................................9-4
Equivalent annual costs..........................................................................................................9-5
2 Capital budgeting under inflation.........................................................................................9-5
Inflation and the discount rate..............................................................................................9-6
Investment bias.......................................................................................................................9-6
Discounting cash flows at the real rate of return.................................................................9-7
Depreciation deductions........................................................................................................9-7
Adjusted real approach..........................................................................................................9-9
3 Capital rationing.....................................................................................................................9-9
Capital constraints and project rankings.............................................................................9-10
Profitability index..................................................................................................................9-10
The ranking of indivisible projects......................................................................................9-11
Multi-period capital rationing..............................................................................................9-11
Further perspectives on capital rationing...........................................................................9-13
4 Assessed tax losses................................................................................................................9-14
The utilisation of assessed losses.........................................................................................9-14
New ventures and ring-fencing provisions..........................................................................9-15
Synopsis..................................................................................................................................9-16
5 Abandonment value and optimal economic lives...............................................................9-16
Continuing evaluation..........................................................................................................9-16
Optimal economic life..........................................................................................................9-17
Replacement timing..............................................................................................................9-18
6 Real (strategic) options........................................................................................................9-20
Examples of real (strategic) options....................................................................................9-21
7 Capital budgeting: a behavioural finance perspective.......................................................9-22
Self-study problems...............................................................................................................9-26
Solutions to self-study problems..........................................................................................9-27
Summary................................................................................................................................9-29
Appendix 9.1 The timing of cash flows, XNPV and XIRR...............................................9-30
Appendix 9.2 Capital budgeting in the real world.............................................................9-32
Appendix 9.3 Multiple internal rates of return..................................................................9-35
Questions...............................................................................................................................9-37
Chapter 10 Capital budgeting: Risk analysis..........................................................................10-1
A golden sunset..........................................................................................................................10-1
Learning objectives.....................................................................................................................10-1
Introduction................................................................................................................................10-2
1 Traditional measures of risk...............................................................................................10-2
Expected value and probability distributions......................................................................10-3
The Hillier model for multiple periods...............................................................................10-5
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2
3
4
5
6
7
8
9
10
11
12
A note on expected values, probabilities and firm size......................................................10-7
Decision trees........................................................................................................................10-8
Certainty equivalents..........................................................................................................10-11
Sensitivity analysis.............................................................................................................10-12
Break-even analysis............................................................................................................10-14
Zero net present value........................................................................................................10-14
Accounting break-even analysis.........................................................................................10-15
Scenario analysis................................................................................................................10-16
Abandonment and expansion.............................................................................................10-16
Monte Carlo simulation.....................................................................................................10-18
The capital asset pricing model.........................................................................................10-19
Project beta of an all-equity firm.......................................................................................10-20
Financial leverage and project betas.................................................................................10-21
More on market risk...........................................................................................................10-22
Risk-adjusted discount rates versus certainty equivalents.............................................10-23
Risk-adjusted discount rates versus the weighted-average cost of capital....................10-23
Further thoughts on risk analysis in capital budgeting..................................................10-24
Future uncertain cash outflows..........................................................................................10-24
Volatility and risk – a case study........................................................................................10-24
Corporate strategy and project risk...................................................................................10-26
Project management, project failure and other factors...................................................10-29
Self-study problems.............................................................................................................10-31
Solutions to self-study problems........................................................................................10-33
Summary..............................................................................................................................10-38
Appendix 10.1 Capital budgeting – risk analysis with Excel®........................................10-39
Scenario Manager...............................................................................................................10-39
Tornado graphs in Excel.....................................................................................................10-40
Data tables...........................................................................................................................10-41
Goal Seek............................................................................................................................10-41
Form controls......................................................................................................................10-42
Probability distributions.....................................................................................................10-42
Monte Carlo simulation with Excel...................................................................................10-43
Questions.............................................................................................................................10-49
Chapter 11 Working capital......................................................................................................11-1
Every cloud has a silver lining...................................................................................................11-1
Learning objectives.....................................................................................................................11-1
Introduction................................................................................................................................11-1
1 What is working capital?......................................................................................................11-2
2 The objective of working capital policy...............................................................................11-3
The working capital cycle.....................................................................................................11-3
The impact of inflation on working capital policy..............................................................11-5
The impact of changes in sales on working capital policy.................................................11-5
3 Working capital policies.......................................................................................................11-5
4 Working capital financing policies......................................................................................11-7
Working capital management by small business............................................................... 11.10
From the real world............................................................................................................11-10
Working capital management around the world..............................................................11-12
5 Working capital strategies and cash flows.......................................................................11-13
6 Forecasting working capital requirements.......................................................................11-15
7 Forecasting sales.................................................................................................................11-17
Factors to be considered.....................................................................................................11-17
Subjective forecasting.........................................................................................................11-18
Objective forecasting..........................................................................................................11-18
Summary..............................................................................................................................11-19
Appendix 11.1 Cash flows, working capital and indirect taxation (VAT).......................11-20
Self-study problem..............................................................................................................11-22
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Solution to self-study problem...........................................................................................11-23
Questions.............................................................................................................................11-23
Chapter 12 Current asset management and short-term financing........................................12-1
Cash is king.................................................................................................................................12-1
Learning objectives.....................................................................................................................12-1
Introduction................................................................................................................................12-1
1 Credit policy..........................................................................................................................12-1
Creditworthiness...................................................................................................................12-2
Setting the collection policy.................................................................................................12-3
Setting settlement discount policy.......................................................................................12-3
Analysing the impact of a change in credit policy on profitability....................................12-3
Analysing the impact of a change in credit policy: net present value analysis.................12-7
2 Accounts receivable management........................................................................................12-8
Making money out of offering credit to customers............................................................12-9
From the real world: Truworths and Mr Price....................................................................12-9
3 Inventory management.........................................................................................................12-9
Inventory models.................................................................................................................12-10
Inventory control systems...................................................................................................12-14
Just-in-time (JIT) inventory management........................................................................12-14
Supply chain management (SCM).....................................................................................12-15
Inventory management and logistics: the case for distribution centres and crossdocking.................................................................................................................................12-16
From the real world: Shoprite............................................................................................12-17
Advantages of distribution centres....................................................................................12-17
Cross-docking......................................................................................................................12-19
4 Cash management...............................................................................................................12-21
Reasons for holding cash....................................................................................................12-21
The management of float, cash concentration and electronic funds transfer................12-21
Cash budgets.......................................................................................................................12-22
5 Financing current assets....................................................................................................12-25
Accruals...............................................................................................................................12-25
Trade credit..........................................................................................................................12-25
Factoring and invoice discounting.....................................................................................12-26
From the real world: Pick n Pay and invoice financing....................................................12-29
Bank overdrafts...................................................................................................................12-29
Bankers’ acceptances (bank bills)......................................................................................12-29
Revolving credit facility......................................................................................................12-30
Repurchase agreements (Repo market)...........................................................................12-31
Short-term financing: advantages and disadvantages......................................................12-32
Summary..............................................................................................................................12-33
Guidance on working capital.............................................................................................12-33
Self-study problems.............................................................................................................12-34
Solutions to self-study problems........................................................................................12-35
Questions.............................................................................................................................12-39
Chapter 13 Sources of finance..................................................................................................13-1
A lion retreats.............................................................................................................................13-1
Learning objectives.....................................................................................................................13-1
Introduction................................................................................................................................13-1
1 Financial markets.................................................................................................................13-2
Money and capital markets..................................................................................................13-2
Primary and secondary markets...........................................................................................13-2
Formal and over-the-counter (OTC) markets....................................................................13-2
Spot and derivative markets.................................................................................................13-2
The Johannesburg Stock Exchange.....................................................................................13-3
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3
4
5
6
7
8
9
10
Alternative Exchange – AltX...............................................................................................13-6
A2X Markets.........................................................................................................................13-7
Alternative methods of obtaining a listing..........................................................................13-8
Raising capital by listed companies.....................................................................................13-8
Setting an issue price............................................................................................................13-8
Rights issue............................................................................................................................13-9
Some facts about market liquidity.....................................................................................13-10
The JSE Derivatives Market..............................................................................................13-11
The JSE Debt Market.........................................................................................................13-11
Financial institutions.........................................................................................................13-13
Banks....................................................................................................................................13-13
Investment institutions.......................................................................................................13-14
Private equity and venture capital.....................................................................................13-14
Special institutions..............................................................................................................13-17
Equity-related instruments................................................................................................13-19
Ordinary shares...................................................................................................................13-19
Retained earnings...............................................................................................................13-20
Preference shares................................................................................................................13-20
Debt instruments................................................................................................................13-22
Corporate bonds, notes and debentures...........................................................................13-22
Long-term loans..................................................................................................................13-24
Bank loans...........................................................................................................................13-24
Fixed interest rate loans.....................................................................................................13-25
Variable interest rate loans................................................................................................13-26
Unsecured notes..................................................................................................................13-27
Foreign loan or bond financing..........................................................................................13-27
Credit ratings.......................................................................................................................13-27
Short-term debt...................................................................................................................13-29
Hybrid instruments............................................................................................................13-29
Comparison of debt and equity.........................................................................................13-30
Return..................................................................................................................................13-30
Risk......................................................................................................................................13-30
Control.................................................................................................................................13-31
From the real world – corporate bonds and borrowings.................................................13-32
Inflation-linked bonds........................................................................................................13-33
Alternative sources of finance............................................................................................13-34
Peer-to-peer lending...........................................................................................................13-35
Crowdfunding......................................................................................................................13-36
Online invoice trading platforms.......................................................................................13-36
Supply chain finance...........................................................................................................13-36
Financing for black economic empowerment (BEE) entities..........................................13-37
From the real world: Sasol and Absa BEE transactions.................................................13-41
Islamic Finance...................................................................................................................13-43
From the real world … Islamic Finance and the JSE......................................................13-43
Guidance when presented with problems relating to sources of finance.......................13-44
Summary..............................................................................................................................13-47
Self-study problems.............................................................................................................13-47
Solutions to self-study problems........................................................................................13-48
Questions.............................................................................................................................13-49
Chapter 14 Capital structure....................................................................................................14-1
Learning objectives.....................................................................................................................14-1
Introduction................................................................................................................................14-2
1 Risk profile............................................................................................................................14-2
Business risk..........................................................................................................................14-2
Financial risk.........................................................................................................................14-3
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2 Leverage (gearing)................................................................................................................14-3
Impact on earnings...............................................................................................................14-4
Impact on risk........................................................................................................................14-4
3 Optimal capital structure....................................................................................................14-8
The Modigliani-Miller approach.........................................................................................14-8
Trade-off theory..................................................................................................................14-11
Pecking order and signalling theories................................................................................14-13
Debt financing, free cash flow and conflicts between management and shareholders....14-13
4 Agency costs and inverted incentives: conflicts between shareholders
and bondholders.................................................................................................................14-14
Investing in high-risk projects............................................................................................14-14
Running off with the money...............................................................................................14-15
No further investment by shareholders.............................................................................14-15
Playing for time...................................................................................................................14-15
Changing the capital structure of the firm........................................................................14-16
The use of loan covenants to manage shareholder and bondholder conflicts...............14-16
From the real world: Loan covenants at Aspen and Gold Fields...................................14-17
5 The impact of inflation.......................................................................................................14-17
6 The need for flexibility.......................................................................................................14-18
Target capital structure.......................................................................................................14-18
Short-term deviation from target.......................................................................................14-18
Financial flexibility..............................................................................................................14-19
Market timing theory..........................................................................................................14-19
7 Debt and tax shields...........................................................................................................14-20
8 Financial leverage and a firm’s weighted-average cost of capital..................................14-23
9 Personal taxes.....................................................................................................................14-24
10 Capital structures in South Africa and around the world..............................................14-25
From the real world............................................................................................................14-27
11 Edcon: Capital structure and valuation of tax shields....................................................14-29
12 Capital structure decisions - a behavioural finance perspective....................................14-31
Summary..............................................................................................................................14-32
Guidance on capital structure............................................................................................14-32
Appendix 14.1 Global debt and debt-equity ratios..........................................................14-35
Self-study problem..............................................................................................................14-37
Solution to self-study problem...........................................................................................14-37
Questions.............................................................................................................................14-38
Chapter 15 Leasing....................................................................................................................15-1
Leasing in the airline sector is no laughing matter..................................................................15-1
Learning objectives.....................................................................................................................15-1
Introduction................................................................................................................................15-2
1 Types of leases.......................................................................................................................15-2
Direct lease............................................................................................................................15-2
Sale and lease-back...............................................................................................................15-2
Leveraged lease.....................................................................................................................15-3
2 Off-balance sheet financing and leasing.............................................................................15-3
3 The accounting for leases in terms of IFRS 16..................................................................15-4
The effect of IFRS 16 on financial statements, ratios and processes..............................15-5
Is a contract a lease or does the contract contain a lease?................................................15-6
Non-lease components.........................................................................................................15-7
Lease term, lease payments and the discount rate.............................................................15-8
Structuring considerations....................................................................................................15-8
Application of IFRS 16: an example...................................................................................15-9
4 Advantages of leasing.........................................................................................................15-10
Changing technology...........................................................................................................15-10
Tax advantages.....................................................................................................................15-11
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Obtaining 100% debt financing.........................................................................................15-11
Operating flexibility............................................................................................................15-11
Reduction in operating leverage........................................................................................15-11
Coping with uncertain demand..........................................................................................15-11
Specialisation effects on maintenance, residual values and purchase costs...................15-12
Standardisation of contracts...............................................................................................15-12
Fewer restrictions................................................................................................................15-12
Off-balance sheet financing................................................................................................15-12
Avoidance of capital expenditure controls and budgetary constraints...........................15-12
5 Evaluating the leasing decision.........................................................................................15-12
Selecting an appropriate discount rate..............................................................................15-13
Calculating the net present cost.........................................................................................15-14
The present cost of leasing.................................................................................................15-14
The present cost of borrowing and buying........................................................................15-14
The net advantage of leasing and NPV.............................................................................15-16
From the real world............................................................................................................15-18
6 The adjusted present value approach...............................................................................15-20
Summary..............................................................................................................................15-22
Self-study problems.............................................................................................................15-22
Solutions to self-study problems........................................................................................15-23
Appendix 15.1 Operating lease capitalisation and other pertinent leasing issues.........15-27
Questions.............................................................................................................................15-30
Chapter 16 Dividends and share buy-backs............................................................................16-1
The dividend cut that made headlines around the world........................................................16-1
Learning objectives.....................................................................................................................16-2
Introduction................................................................................................................................16-2
1 Dividend relevance – active variable or passive residual?................................................16-2
The residual approach to dividends....................................................................................16-3
2 Factors affecting the dividend decision..............................................................................16-7
The legal requirements of the Companies Act 71 of 2008: solvency and liquidity tests....16-7
Contractual obligations........................................................................................................16-8
Information content of dividends........................................................................................16-8
Taxation................................................................................................................................16-10
The nature of shareholders................................................................................................16-12
3 Dividend payment policies.................................................................................................16-12
Stable dividend amount......................................................................................................16-12
Stable payout ratio..............................................................................................................16-13
Special dividends.................................................................................................................16-14
Stable dividend plus special dividend................................................................................16-15
4 The payment of dividends..................................................................................................16-16
What happens to the share price when a share goes ex-dividend?.................................16-17
Share splits and capitalisation issues.................................................................................16-18
From the real world: Sub-division of the ordinary share capital of Assore...................16-19
Dividend reinvestment plans (DRIPs) and scrip dividends.............................................16-20
5 Share buy-backs..................................................................................................................16-21
What is the effect of a share buy-back on the Statement of Financial
Position of a company?.......................................................................................................16-22
Why should companies repurchase their own shares?.....................................................16-22
Requirements and consequences of engaging in a share buy-back.................................16-23
From the real world............................................................................................................16-25
Dividends in specie..............................................................................................................16-26
Dividend yields....................................................................................................................16-27
How important are dividends to investor returns............................................................ 16.29
Dividend policy and share repurchases: what is the evidence in South Africa..............16-30
From the real world … AB InBev cuts dividend..............................................................16-31
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Summary..............................................................................................................................16-31
Analysing the distribution decision – guidance and practical application......................16-32
Self-study problems.............................................................................................................16-35
Solutions to self-study problems........................................................................................16-36
Questions.............................................................................................................................16-38
Chapter 17 Mergers, acquisitions and corporate restructuring............................................17-1
Out of Africa: SABMiller is acquired by AB InBev................................................................17-1
Learning objectives.....................................................................................................................17-1
Introduction................................................................................................................................17-2
1 Types of mergers...................................................................................................................17-2
2 Reasons for mergers.............................................................................................................17-2
Operating economies............................................................................................................17-2
Managerial skills...................................................................................................................17-3
Tax considerations – tax shield and assessed losses............................................................17-3
Use for excess liquidity.........................................................................................................17-4
Diversification.......................................................................................................................17-4
Lower financing costs...........................................................................................................17-4
Replacement costs................................................................................................................17-4
Technology.............................................................................................................................17-4
Products, product pipeline and reserves.............................................................................17-4
3 The structuring of takeover offers and taxation................................................................17-5
Financing costs......................................................................................................................17-5
Capital Gains Tax (CGT) and Dividend Withholding Tax (DWT)...................................17-5
Depreciation and wear and tear deductions.......................................................................17-6
Further issues to consider in acquiring shares or assets....................................................17-6
4 Are mergers successful?.......................................................................................................17-7
Mergers and acquisitions: a behavioural finance perspective...........................................17-8
5 Terms of mergers..................................................................................................................17-9
Acquisition financed by cash................................................................................................17-9
Free cash flow (discounted cash flow) analysis................................................................17-10
Minimum and maximum values.........................................................................................17-11
Acquisition financed by share issue...................................................................................17-11
Synergy.................................................................................................................................17-12
Post-merger price-earnings ratio.......................................................................................17-14
Sharing the merger benefit.................................................................................................17-15
Setting an offer....................................................................................................................17-17
6 Dividends, working capital and net asset value...............................................................17-17
Dividends.............................................................................................................................17-17
Working capital...................................................................................................................17-18
Net asset value....................................................................................................................17-18
7 Reverse takeovers................................................................................................................17-18
8 Defensive tactics..................................................................................................................17-18
Proactive measures.............................................................................................................17-18
Reactive measures...............................................................................................................17-20
9 Legal procedures.................................................................................................................17-21
10 Regulation of takeovers......................................................................................................17-22
11 Unbundling, spin-offs and demergers...............................................................................17-25
Advantages..........................................................................................................................17-26
Disadvantages......................................................................................................................17-26
12 Leveraged buy-outs.............................................................................................................17-27
13 Business rescue and the corporate restructuring of financially troubled companies.....17-29
Financial distress.................................................................................................................17-29
Is business rescue a viable option?....................................................................................17-31
Financial distress, capital structure theory and agency relationships.............................17-31
The priority rule in liquidations.........................................................................................17-32
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The direct costs of bankruptcy/liquidation and business rescue.....................................17-33
Workouts..............................................................................................................................17-33
What can the directors do to improve the chances of success of a business rescue......17-34
Advising a financially troubled company..........................................................................17-34
Causes of financial trouble.................................................................................................17-34
Some solutions....................................................................................................................17-35
Summary..............................................................................................................................17-36
Self-study problem..............................................................................................................17-37
Solutions to self-study problem.........................................................................................17-38
Appendix 17.1 Mergers and acquisitions – an overview and alternative approach
to calculate exchange ratios...............................................................................................17-40
Appendix 17.2 Due diligence.............................................................................................17-42
Appendix 17.3 Business rescue in South Africa...............................................................17-46
Appendix 17.4 South African mergers and demergers....................................................17-49
The hostile Nedcor bid for Standard Bank Investment Corporation.............................17-50
The JD Group, Ellerines and African Bank.....................................................................17-50
BHP Billiton........................................................................................................................17-51
The hostile Harmony takeover bid for Goldfields...........................................................17-51
The takeover of ABSA by Barclays plc.............................................................................17-52
MTN acquisition of Investcom LLC..................................................................................17-53
The unbundling of Goldfields’ gold mines into Sibanye Gold........................................17-54
The battle for Adcock Ingram...........................................................................................17-54
Woolworths’ acquisition of David Jones...........................................................................17-56
The Sibanye acquisitions of Stillwater and Lonmin.........................................................17-56
BHP Billiton and South32..................................................................................................17-58
Walmart Stores acquires control of Massmart..................................................................17-59
Questions.............................................................................................................................17-60
Chapter 18 Risk management and derivatives........................................................................18-1
What does Warren Buffett think about derivatives?...............................................................18-1
Learning objectives.....................................................................................................................18-1
Introduction................................................................................................................................18-2
1 Risk management strategies................................................................................................18-2
Interest rate risk....................................................................................................................18-3
Refinancing risk....................................................................................................................18-3
Liquidity risk.........................................................................................................................18-4
Currency risks........................................................................................................................18-5
Credit risk..............................................................................................................................18-5
Market and commodity price risks......................................................................................18-6
General risks.........................................................................................................................18-6
2 Rationale for financial innovation......................................................................................18-7
3 Fundamental derivative instruments..................................................................................18-8
Options..................................................................................................................................18-8
Valuation of options..............................................................................................................18-9
Replicating portfolio...........................................................................................................18-11
Black-Scholes Option Pricing Model.................................................................................18-13
Put-call parity......................................................................................................................18-15
Using Excel® to determine Black-Scholes option values................................................18-15
The Binomial Option Pricing Model.................................................................................18-16
Options, the Greeks and implied volatility.......................................................................18-19
Futures and forward contracts...........................................................................................18-20
Pricing of futures and forward contracts...........................................................................18-22
4 Risk-reducing techniques...................................................................................................18-23
Natural hedges (operational hedging)..............................................................................18-24
Hedging with futures, forwards, and options....................................................................18-25
From the real world: Hedging by South African companies...........................................18-26
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What does Warren Buffett think?......................................................................................18-29
Contracts for difference (CFD).........................................................................................18-29
Interest rate risk..................................................................................................................18-32
Hedging with interest rate swaps.......................................................................................18-32
Duration and immunisation...............................................................................................18-35
Hedging interest risk with Floors, Caps and Collars........................................................18-38
From the real world: The Foschini Group........................................................................18-42
Derivative use by South African companies.....................................................................18-42
The JSE South African Volatility Index (SAVI): The “Fear” Index...............................18-44
5 Return-generating techniques...........................................................................................18-45
Securitisation.......................................................................................................................18-45
Tax arbitrage........................................................................................................................18-47
Convertible securities.........................................................................................................18-47
Summary..............................................................................................................................18-48
Appendix 18.1 Employee share options/share-based payments......................................18-49
From the real world............................................................................................................18-52
Appendix 18.2 Option trading strategies..........................................................................18-52
Appendix 18.3 A short introduction to hedge funds........................................................18-56
Self-study problem..............................................................................................................18-58
Solution to self-study problem...........................................................................................18-58
Questions.............................................................................................................................18-58
Chapter 19 International financial management....................................................................19-1
The end of the affair..................................................................................................................19-1
Learning objectives.....................................................................................................................19-1
Introduction................................................................................................................................19-1
1 Historical perspective...........................................................................................................19-2
2 The balance of payments......................................................................................................19-4
Current account....................................................................................................................19-4
Capital account.....................................................................................................................19-4
Official reserves.....................................................................................................................19-4
3 The foreign exchange market...............................................................................................19-4
Direct and indirect quotations.............................................................................................19-5
Bid–ask spread......................................................................................................................19-5
Mid-rate.................................................................................................................................19-6
Spot and forward transactions.............................................................................................19-6
Points......................................................................................................................................19-6
Forward rate and premium/discount...................................................................................19-6
Cross rates.............................................................................................................................19-7
4 Forces behind exchange rate movements............................................................................19-7
Interest rate parity................................................................................................................19-7
The purchasing power parity theory (PPP).........................................................................19-9
Big Mac exchange rates......................................................................................................19-11
Integrating the interest rate parity and purchasing power parity theories.....................19-12
Forecasting, forward rates and exchange rate volatility...................................................19-13
5 Foreign exchange exposure................................................................................................19-16
Translation exposure...........................................................................................................19-16
Transaction exposure..........................................................................................................19-18
Economic exposure.............................................................................................................19-18
From the real world............................................................................................................19-19
6 Hedging policies..................................................................................................................19-19
Forward contract.................................................................................................................19-20
Money-market hedge..........................................................................................................19-21
Currency options.................................................................................................................19-23
Currency of invoice.............................................................................................................19-24
Leads and lags.....................................................................................................................19-24
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7
8
9
10
11
12
13
14
Futures contracts.................................................................................................................19-24
Currency swaps....................................................................................................................19-26
Long-term currency swaps..................................................................................................19-26
Valuation of a currency swap.............................................................................................19-28
Short-term currency swaps.................................................................................................19-29
Exchange control................................................................................................................19-29
Covered-interest arbitrage.................................................................................................19-32
The eurodollar market.......................................................................................................19-34
Offshore financing by South African companies.............................................................19-34
Offshore borrowings...........................................................................................................19-34
Listing on foreign stock exchanges....................................................................................19-35
Documentary letters of credit............................................................................................19-35
Analysis of foreign investments.........................................................................................19-37
Determination of future cash flows...................................................................................19-37
Forecasting future exchange rates.....................................................................................19-37
Determination of the discount rate...................................................................................19-38
International portfolio diversification..............................................................................19-40
Analysis of a major project by BHP Billiton....................................................................19-40
Summary..............................................................................................................................19-41
Self-study problem..............................................................................................................19-42
Solution to self-study problem...........................................................................................19-43
Questions.............................................................................................................................19-44
Chapter 20 Business planning and financial modelling.........................................................20-1
It’s a journey, not a destination.................................................................................................20-1
Learning objectives.....................................................................................................................20-1
1 Business plans.......................................................................................................................20-1
What are the advantages of preparing a business plan?....................................................20-2
The content and structure of a business plan.....................................................................20-4
Background/Strategy.............................................................................................................20-5
Products and services............................................................................................................20-6
Markets and marketing strategies........................................................................................20-7
Operations and production process.....................................................................................20-9
Management and executive team......................................................................................20-11
Legal, social and environmental factors............................................................................20-15
Financial information and projections..............................................................................20-15
The components of the financial projections section.......................................................20-17
Projections of statements of comprehensive income.......................................................20-17
Projected statements of financial position........................................................................20-18
Cash flow projections..........................................................................................................20-18
Sensitivity and scenario analysis........................................................................................20-18
Porter’s Five Forces............................................................................................................20-19
What other factors will play a role in the financing decision?........................................20-19
From the real world: Invenfin............................................................................................20-19
From the real world: Industrial Development Corporation............................................20-20
2 Financial modelling............................................................................................................20-21
The design and layout of financial models........................................................................20-21
Avoiding spreadsheet errors..............................................................................................20-23
The use of spreadsheet models in corporate finance.......................................................20-24
The application of ‘what-if’ analysis in Excel®................................................................20-25
Financial models and topics in corporate finance............................................................20-26
3 Financial modelling and forecasting financial statements: An application..................20-26
Goal seek, data tables and sensitivity analysis..................................................................20-34
Tornado graph.....................................................................................................................20-35
Circular references in Excel®............................................................................................20-36
Summary..............................................................................................................................20-37
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Chapter 21 Corporate Strategy and Business Models............................................................21-1
1 Corporate strategy and industry analysis..........................................................................21-1
2 What is strategy?..................................................................................................................21-3
3 Matrix models.......................................................................................................................21-6
Boston Consulting Group & Strategic Business Units (BCG growth-share Matrix)......21-6
General Electric Corporation (GEC) - McKinsey matrix.................................................21-7
Ansoff Product-Market Matrix............................................................................................21-8
4 Michael Porter’s Five Forces model....................................................................................21-8
Rivalry among existing competitors..................................................................................21-10
Threat of new entrants and potential competitors...........................................................21-10
Threat of substitutes...........................................................................................................21-11
The power of customers.....................................................................................................21-12
The power of suppliers.......................................................................................................21-13
Porter’s value chain.............................................................................................................21-14
Porter’s four corners analysis.............................................................................................21-14
5 Other strategic factors.......................................................................................................21-15
Analysis of competitors and customers.............................................................................21-18
Product life cycle.................................................................................................................21-18
6 The building blocks of a business model..........................................................................21-19
Customer segments.............................................................................................................21-19
Value propositions..............................................................................................................21-22
Channels..............................................................................................................................21-25
Customer relationships.......................................................................................................21-27
Revenue streams.................................................................................................................21-28
Key resources......................................................................................................................21-29
Key activities........................................................................................................................21-29
Key partnerships.................................................................................................................21-29
Cost structure......................................................................................................................21-30
7 The resource-based view of the firm...................................................................................21-30
8 Disruptive technologies, 3D printing and the role of big data.......................................21-32
Distributed ledger technology (blockchain) and smart contracts...................................21-36
Digital sensors and contracts.............................................................................................21-37
Summary..............................................................................................................................21-38
Tables........................................................................................................................................... T-2
Index ............................................................................................................................................. I-1
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Preface
The 9th edition is aimed at students undertaking either an introductory or intermediate course
in corporate finance. The objective is to offer students an in-depth view of finance theory and
practice. This edition is up-to-date, relevant and offers insights into the application of financial
theories to maximise value. In the interests of the reader, we have expanded some complex
sections while simplifying others to retain focus. Each chapter begins with learning objectives
to guide the reader through the text, and concludes with self-study problems and detailed
solutions. A number of new questions and self-study problems have been added and we trust
that this will make the book even more useful to those preparing for finance examinations.
In particular, we have added recent ITC questions which reflect the direction that SAICA is
following in setting contextualised integrated questions.
The textbook has been updated to include sections on all the topics set out in SAICA’s
Competency Framework in respect to financial management, financial risk management and
corporate strategy. The book is aligned to Version 10 of the Competency Framework, which was
issued in November 2017 and which is effective from January 2019. Relevant references to the
Companies Act of 2008 have been included such as the solvency and liquidity requirements
and the provisions relating to takeovers and business rescue. We have included a section on
turning around financially troubled companies. In line with the Competency Framework we
have increased our focus on risk management. Where relevant, we have referred to King IV.
Also, in line with the Competency Framework, there is an increased focus on corporate strategy
and business models. There is a separate chapter on business planning and financial modelling.
There is a greater emphasis on support materials such as PowerPoint slides, questions,
the use of Excel models as well as greater reference to applications of finance theory in a
South African context. Major changes in content include new sections on behavioural finance,
retirement planning and living annuities, Value at Risk (VaR), XNPV, XIRR, Exchange Traded
Funds (ETFs), distributed ledgers (blockchain), application of Monte Carlo simulation, and
Islamic Finance. We have included a section on integrated reporting and the six Capitals in
Chapter 5 and we have introduced the resource-based theory of the firm in Chapter 21. We
have expanded the section on failure prediction due to the introduction of the business rescue
provisions of the Companies Act of 2008 and the increased focus on financial distress. In
Chapter 13, we have expanded the section on private equity and and the sections on inflation
linked bonds, the use of repos, revolving credits, and alternative sources of finance such as peerto-peer lending, crowd funding and online invoice trading platforms. We have rewritten Chapter
15 on leasing to include the impact of IFRS 16, which is effective from January 2019. Chapter
18 has been expanded to reflect the growing importance of the use of derivatives. We have
made extensive reference to financial decision-making by South African companies and each
chapter includes a section entitled ‘From the real world…’ which sets the topic in relation to
the experience or actions of a South African company. We have often referred to what Warren
Buffett thinks about a particular topic.
We have made extensive references to the JSE’s equity market, the JSE’s debt market and
the JSE’s derivatives market. We have endeavoured to offer an integrated view of finance, yet
we invite students to challenge conventional wisdoms. The focus is on financial decision-making
which will maximise the value of a company.
This edition has been influenced by the feedback I have received from colleagues and
tutors, and I would like to thank all who provided valuable suggestions. I am grateful for the
insights provided by the contributors to the book and am always indebted to the founding
authors. I am grateful to Ross Compton for sourcing research data, Carlyn Bartlett-Cronje
and Chris Lawrence at Juta for managing the publication process and Wouter Reinders for
typesetting. I would like to thank Tarryn Witten, Edith Viljoen and Helen Correia for editing
and proof-reading each chapter.
Carlos Correia
Emeritus Professor, University of Cape Town
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What does the book offer?
LEARNING OBJECTIVES
We have included learning objectives at the beginning of each chapter. Students can
use these to view the key issues that are covered in the chapter. Students can also test
themselves at the end of each chapter on whether these learning objectives have been realised.
REAL WORLD EXAMPLES AND REFERENCES TO LISTED SOUTH AFRICAN
COMPANIES
We have included many real world examples and have made reference to listed South African
companies. The objective is to show how South African companies use corporate finance
in practice and to indicate the relevance of finance in the real world. For example, we have
included the application of time value of money principles to pensions and retirement
planning and have valued the contracts of Ronaldo and Messi. We have valued Woolworths,
analysed the dividend policy of Anglo American and analysed the share buy-backs by
Vodacom. We study the integrated report of Truworths and compare its return on invested
capital to its cost of capital. We analysed the capital structure and cost of capital of Sasol and
determined the economic profit of Distell. We explained the unbundling of Sibanye Gold from
Gold Fields and the distribution of South32 as a dividend in specie. We examined the dividend
policy of Shoprite and analysed the performance of Massmart and Walmart and the valuation of
Pepkor and Steinhoff. We designed a financial model in order to value Clicks. We have analysed
the leveraged buy-out of Edcon by Bain Capital and we have valued Eskom bonds. We have
also analysed developments in the South African corporate bond market, the JSE, the AltX
and the JSE’s derivatives market. We have analysed the performance of the NewGold ETF
relative to buying gold mining shares. We analyse the composition and requirements of the
JSE Shariah Indices.
USE OF WORKED EXAMPLES TO EXPLAIN CORPORATE FINANCE CONCEPTS
We have endeavoured to clearly explain the underlying concepts of corporate finance but
believe that it is important to also use worked examples in each chapter to indicate how to
apply these concepts. In most cases, such examples are concise and focus on a particular concept in each chapter.
EXTENSIVE USE OF EXCEL SPREADSHEET MODELS
We believe that students should not only understand corporate finance but should also be able
to use Excel spreadsheets to solve many finance applications. This reflects the use of Excel
models in practice and will enable students to go out into the corporate environment with a
useful knowledge of how to use Excel spreadsheets to solve corporate finance problems, which
will offer them a competitive edge. For example, students are required to use Excel to solve
time value of money problems, such as pension plans and loan amortisation schedules. Excel is
employed to value corporate bonds and ordinary shares. Students are required to use Excel in
capital budgeting and forecasting future cash flows. The text explains how to use Excel in risk
analysis and how to build simple Monte Carlo simulation models. Excel is employed to value
options based on the Black-Scholes and Binomial pricing models. We have included in Chapter
20 a section on financial modelling, focusing on the design and application of spreadsheet
models.
USE OF FINANCIAL CALCULATORS
In Chapter 2, we have included a section on how to use financial calculators to solve time
value of money problems and have explained how financial calculators can be used to discount
future cash flows. We have solved problems with formulas and tables and have used the same
examples in explaining the use of financial calculators. We also offer a Guide to Financial
Calculators by Colin Smith, a senior lecturer at UCT, on how to use financial calculators. This
guide may be downloaded at Juta. Please refer to the inside cover for the URL for the book.
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USE OF SELF-STUDY EXAMPLES AT THE END OF CHAPTERS
At the end of each chapter there are comprehensive self-study examples with worked solutions.
This is to reinforce what has been covered in that chapter and prepares students to embark
upon the problems at the end of the chapter.
EXTENSIVE NUMBER OF STRAIGHTFORWARD AND COMPLEX PROBLEMS AT THE
END OF EACH CHAPTER
At the end of each chapter there are a large number of straightforward and complex questions
and problems. The ability to answer these problems will indicate a high level of understanding
of financial management.
PROFESSIONAL EXAMINATION QUESTIONS
We have included a significant number of professional examination questions from the Initial
Test of Competence (ITC) examinations as well as prior Qualifying Examination questions
set by the South African Institute of Chartered Accountants (SAICA). We have also included
questions from ACCA and CIMA. The inclusion of professional questions as well as
the inclusion of complex questions at the end of each chapter (as well as the additional
questions on the financial management website) assists students to prepare for professional
examinations. The majority of the integrated questions are sourced from SAICA’s ITC and
Qualifying Examinations. Any specimen questions and solutions released by SAICA relating to
the ITC will be made available on the book’s website and then clearly referenced with respect to
financial management topics assessed therein.
TEXTBOOK IN LINE WITH SAICA’S COMPETENCY FRAMEWORK
SAICA initially issued its Competency Framework for Chartered Accountants in 2009. The
objective was to ensure that there will be a greater contextualisation and integration of topics
as well as a greater focus on corporate strategy and risk management in the examination of
Financial Management. This edition has expanded the sections on corporate strategy and risk
management and offers advanced questions in each chapter in order to offer a greater level
of contextualisation in line with the Competency Framework. The Competency Framework
was amended in November 2017 when SAICA issued Version 10 of the Framework, which will
be effective from January 2019. We have aligned this book to Version 10 of the Competency
Framework. We have offered a detailed explanation of this in a separate section and have set out
each competency for the Strategy, Risk Management (in respect to financial risk management)
and Financial Management areas and we set out where we deal with each specific competency
in the book. We have endeavoured to ensure that we have covered Financial Management and
Strategy and Financial Risk Management topics and we refer each topic in the Knowledge
Reference List to a particular chapter in the book. SAICA’s CA2025 Project is expected to lead
to changes in the Competency Framework over the next few years. As far as this effects financial
management and corporate strategy, we will use the book’s website to expand the scope of the
textbook to ensure we remain in compliance with future developments.
Although the textbook is primarily addressing the requirements of the ITC, the expansion of
the topics relating to corporate strategy, business models, business planning, risk management
and practical issues of financial decision-making, will make the book increasingly relevant for
candidates preparing for the Assessment of Professional Competence (APC) examination.
INTEGRATION OF TOPICS
We have endeavoured to integrate topics and show how chapters are linked. For example,
the use of the dividend discount model in Chapter 6 to value a company’s shares is linked to
the growing perpetuity formula in Chapter 2. We also integrate cost of capital (chapter 7) with
valuations (chapter 6) and with capital structure (chapter 14) by referring to each topic relative
to each other.
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EASE OF USE AND FLEXIBILITY
Although we have tried to integrate topics, for pedagogical reasons, we have also been conscious that students will not cover all the topics in a standard unit on corporate finance. We
have used our experience in the classroom to ensure that some topics are separate and stand
on their own for the purpose of structuring course programmes and ensuring flexibility.
FOCUS ON STRATEGY
Financial management is about financial decision-making and we have gone further than other
textbooks to integrate corporate strategy into corporate finance. This is because we understand
the importance of strategic issues in financial decision-making. We have written extensively
on corporate strategy in Chapters 1, 20 and 21 and within other chapters as we have placed
financial decision-making within the context of a company’s strategy. This means that we have
complied with the requirements of the Competency Framework in relation to corporate strategy,
which is included in SAICA’s Strategy, Risk Management and Corporate Governance competency
area. Questions in the ITC increasingly require analysis of a corporate situation or transaction.
Understanding corporate strategy will better prepare candidates to address these types of questions. Furthermore, companies are outlining their corporate strategy in their integrated reports
and we need to understand what strategy is (and what it is not) when we analyse integrated
reports. This also means that sometimes we need to adapt financial theory to a company’s strategic intent. For example, Sasol had a very low debt-equity ratio, which was not optimal in terms
of financial theory. Yet, Sasol was able to effectively finance its plans to expand internationally
within the next few years, which was a key component of its strategy.
BEHAVIOURAL FINANCE
Behavioural Finance analyses the psychology of financial decision-making. We have included
sections on behavioural finance in numerous chapters in the book. We focus on identifying biases
and the mental short-cuts that may lead to non-optimal financial decision-making. We propose
solutions so that you apply the right techniques, the right strategy, and the right approach to
manage biases and heuristics in making financial decisions.
BUILDING-BLOCK APPROACH
We have used a building-block approach to corporate finance whereby we build on the
fundamental concepts of finance and increase the complexity of each topic step-by-step in each
chapter. This enables units to be structured with flexible levels of complexity so that units may
be limited to a number of sections in each chapter. We have also used appendices partly for
the same reason.
GUIDANCE TO KEY TOPICS IN FINANCIAL MANAGEMENT
We have included guidance notes to students at the end of key chapters in order to assist and
prepare students to effectively deal with particular topics in examinations. Further, the guidance
to these key topics will enable students to better understand and integrate key areas of financial
management. The guidance sections have been written by Johnathan Dillon who brings his
extensive lecturing experience as well as his involvement in SAICA’s examination processes to
effectively assist students with these guidance notes to key chapters.
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What resources does the book offer to the
instructor?
Instructors are provided with a comprehensive Instructor’s Manual, available on the dedicated
website at www.jutaacademic.co.za. Instructors will be able to obtain a username and password
to access this site by registering at www.jutaacademic.co.za. Instructors will find the previous
section on what the textbook offers to be useful for course design and evaluating student performance. We understand the increasing demands placed upon academics and have endeavoured
to ensure that this edition supports the teaching objectives of academic instructors.
The textbook provides learning objectives, worked examples, clarity in writing, self-study
examples and a comprehensive number of end-of-chapter problems. There are references to
up-to-date, real world applications.
The Instructor’s Manual or Instructor’s section of the book’s website includes the following:
COMPLETE SOLUTIONS TO END-OF-CHAPTER QUESTIONS
A complete set of solutions to the end-of-chapter questions are provided in Adobe Acrobat
and Word format. Many questions have been used in a classroom setting and the solutions
reflect feedback received from students.
MCQ TESTS AND SOLUTIONS
Instructors currently have access to a series of MCQ tests and solutions, which they are able
to use if needed. These are available on the Instructor’s section of the book’s website. We are
planning to expand this into a system of assessment for students undertaking a course in financial
management.
EXCEL SPREADSHEET SOLUTIONS
Instructors are provided with selected Excel solutions to end-of-chapter problems. This will
enable instructors to quickly alter variables to point out the effects on solutions. It will also
enable instructors to easily change the data in questions for examination purposes. There are
also Excel solutions for selected worked examples within each chapter.
ADDITIONAL QUESTIONS AND SOLUTIONS NOT IN THE TEXTBOOK
The website includes additional questions and solutions not included in the textbook. This
offers instructors flexibility in assessment and enables changes in the set of questions used
from year-to-year.
POWERPOINT SLIDES
A full set of PowerPoint slides is available to prescribing institutions. The slides have been prepared by the authors and are relevant and up-to-date and follow the content of each chapter.
EMAIL SUPPORT
Lecturers prescribing the textbook can email Carlos at carlos.correia@uct.ac.za for further
explanations or clarification in relation to the content, questions or solutions.
WEBSITE FOR FINANCIAL MANAGEMENT
Juta & Co will maintain a companion website at www.jutaacademic.co.za for the 9th edition of
Financial Management, whereby lecturers will be able to download PowerPoint slides, updated
solutions, readings and other material.
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READINGS, SURVEYS AND BETAS
The instructor’s section of the book’s website includes the AIFMRM report which sets out the
betas of South African listed companies. We have also included the PwC Valuation Methodology
Surveys and the KPMG Cost of Capital Survey. The impact of labour industrial action on the
South African economy and business in general means that it is important to have some insight
into the workings of labour legislation, the labour relations framework and unions. This is
particularly relevant in respect to ITC questions, which refer either directly or indirectly to
labour issues and students are required to present an analysis into how to deal with labour issues.
In order to address this issue, we have included a report on the labour framework in South Africa
on the book’s website which instructors are welcome to download and use as required.
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How does the book fit in with SAICA’s
Competency Framework and the Companies Act?
SAICA’S COMPETENCY FRAMEWORK
The South African Institute of Chartered Accountants (SAICA) introduced a Competency
Framework, which sets out the required competencies of Chartered Accountants at the point of
writing the Initial Test of Competence (formerly known as SAICA’s Part I Qualifying Examination).
The Initial Test of Competence (ITC) is an assessment of core technical knowledge and therefore
SAICA produced a document entitled “Detailed Guidance for the Academic Programme” (referred
to as the Competency Framework), which sets out the competencies and associated knowledge
required at the point of writing the ITC. This section summarises important aspects of SAICA’s
Competency Framework, most notably Version 10 thereof issued in November 2017 (effective
from January 2019).
In writing the 9th edition of Financial Management, we have as far as possible included the
changes relating to SAICA’s most recent Competency Framework (Version 10). In addition, we
have matched the specific Strategy and Financial Management competencies set out in SAICA’s
Competency Framework with the relevant chapters in the Financial Management textbook.
SAICA’s Competency Framework also includes a Knowledge Reference List for each
competency area, which sets out the content and levels of knowledge required to acquire the
specific competencies. We have matched the Knowledge Reference Lists relating to Strategy and
Financial Management to the relevant chapter(s) in the Financial Management textbook.
Ethics & Professionalism
In the Competency Framework SAICA has detailed pervasive qualities and skills required of all
Chartered Accountants, being Ethical Behaviour and Professionalism, Personal Attributes and
Professional Skills. We have included an Appendix in Chapter 1 on Professional Ethics which
follows the Code of Professional Conduct of SAICA. The Chartered Financial Analyst (CFA)
Institute has issued a Code of Ethics and Standards of Professional Conduct to guide the actions
of investment professionals which has been summarised in the same Appendix. Over time, we
expect a greater integration of ethics and financial management.
Integration of Information and Information Technology
SAICA’s Competency Framework requires the integration of information technology (IT) within
the specific competencies as information and IT have become pervasive in the tasks undertaken
by Chartered Accountants. IT is critical for financial management and without the advances in
IT, both in terms of software, models and systems, the functioning of capital markets would be
severely curtailed and the design of financial instruments would be compromised.
The focus on IT in a financial management environment is highly dependent on financial
models. Applications such as option pricing models, bond pricing, loan amortisations and
Monte Carlo simulation are dependent on programs such as Excel and Excel-based models and
programs such as Crystal Ball©. Capital budgeting, mergers and acquisitions, and valuations are
highly dependent on setting up detailed cash flow forecasts in Excel and the use of tools such as
Tornado graphs, Data Tables, Scenario Manager and Monte Carlo simulation.
In the Financial Management textbook, we have focused mainly on the use of Financial
Modelling and the use of Excel to solve financial management applications. We also refer to the
strategic importance and role of IT in a company’s business model.
We employ financial models throughout the textbook, to solve time value of money
applications such as loan amortisations, in risk and return and portfolio theory to determine such
aspects as standard deviations and efficiency frontiers, in capital budgeting to set out project cash
flows and compute NPV and IRR as well as undertake Monte Carlo Simulations. We employ
Excel in determining the cost of capital, valuations of bonds and equities, the determination of
yield to maturity (YTM), Free Cash Flow models, and we make use of Excel models to apply the
Black & Scholes option pricing model.
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Financial modelling is placed in a separate chapter (Chapter 20), where we focus on the
proper design and layout of financial models to optimise flexibility and reduce the potential for
errors, set out model documentation, apply audits of models, and explain the application of such
tools as data tables, goal seek, and scenario manager. We have included a section on the use
of financial modelling to forecast financial statements, determine free cash flows and financing
flows and determine the value of a company. The focus is on the use of financial modelling skills
to solve real world corporate finance applications.
Strategy, Risk Management and Governance
The Competency Framework refers to Strategy, Risk Management and Governance as a specific
competency area. Whilst many sections of this competency area, such as IT strategy, nonfinancial risk management and governance models, are beyond the scope of the Financial
Management textbook, we have addressed specific issues in the 9th edition relating to the Strategy
competencies. Chapter 21 covers various aspects of strategy and strategic models, as well as
the building blocks of a business model. The content covered in Chapter 21 is supported by
real world examples of strategy in practice and builds on Chapter 1 which includes a section on
corporate strategy covering Porter’s Five Forces model, SWOT analysis and PESTEL analysis.
Chapter 1 includes an Appendix dealing with stakeholders and corporate citizenship.
The Financial Management textbook predominantly focuses on risk management relating to
financial risks in line with SAICA’s Competency Framework (Version 10), which now specifically
includes a Financial Management competency entitled “Management of financial risks as part
of the entity’s risk management policy”. Chapter 1 includes a section on risk management while
aspects of risk assessment are also included in Chapter 5 dealing with financial analysis. Although
Chapter 18 and Chapter 19 focus on financial risks, the introduction to Chapter 18 includes an
overview of risk management. A section on aspects of Corporate Governance and King IV is
included in Chapter 1.
THE COMPANIES ACT (NO. 71 OF 2008)
The Financial Management textbook includes reference to the Companies Act of 2008 (Act
71 of 2008) to the extent that this is relevant to financial management. This is in line with
the requirements of SAICA’s Competency Framework, which requires that knowledge of the
Companies Act is determined by the extent required by the specific competency area, in this case
being Financial Management.
The main areas of the Companies Act that has been included in the 8th edition are:
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
■■
Types of companies – differences between private and public companies;
Share capital/stated capital – the use of no par value shares;
Solvency and liquidity tests;
Financial assistance for the purchase of shares;
Distributions to shareholders;
Share buy-backs / subsidiary acquiring company’s shares;
Issuing shares;
Pre-emptive rights to subscribe for shares (rights issues) / capitalisation issues;
Sale of the greater part of a company’s assets;
Mergers and fundamental transactions;
Scheme of arrangement;
Takeovers, mandatory offers, and the Takeover Regulation Panel; and
Business rescue as an alternative to a private workout and liquidation.
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SPECIFIC COMPETENCIES LISTED IN SAICA’S COMPETENCY FRAMEWORK
AND THE SUPPORTING KNOWLEDGE REFERENCE LISTS RELATING TO
STRATEGY AND FINANCIAL MANAGEMENT
Competency levels:
Level A = Awareness; Level I = Initiates the task; Level X = Executes the task
Knowledge levels:
Level 1 = Basic; Level 2 = Intermediate; Level 3 = Advanced
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Competency and Knowledge Levels
SAICA’s Competency Framework sets out what is indicated by the competency levels and
knowledge levels as follows:
COMPETENCY LEVELS
Level A (Awareness)
Requires an awareness of the key ideas and principles within the area. Demonstration of technical
expertise or detailed knowledge in this area is not required. The candidate identifies and explains
the significance of the competency, and the types of circumstances in which it would arise or be
applied.
Level I (Initiates the Task)
Demonstrates an understanding of the requirements of the task and identifies and applies the
required professional skills, including basic quantitative and qualitative analysis, to perform the
task on a preliminary basis (recognising that a review by more senior staff is still necessary).
An intermediate understanding of the subject matter is required. Complex calculations are not
required. Integration with other competencies is straightforward and is of limited complexity.
Level I include level A proficiencies.
Level X (Completes the Task)
Completes all elements of a specified task successfully; therefore, an advanced understanding
of the subject matter is required. Relevant pervasive skills and reflective capacity should be
demonstrated at an advanced level. Technical skills expected to be demonstrated at this level
include, for example, performing complex calculations and concluding on an appropriate course
of action. Proficiency at level X is demonstrated when the problem is clearly identified and
thoroughly analysed, or when a situation is evaluated and useful recommendations are made.
This level of proficiency includes levels A and I proficiencies.
KNOWLEDGE LEVELS
Level – Basic
Summary: Core / essence of the subject matter
■■ Includes: Significance, relevance, defining attributes
■■ Excludes: Detail, including procedural or numerical aspects
■■ Objective: Enable candidate to recognise issues when encountered and to seek further depth
Level 2 – Intermediate
Summary: Central ideas and issues that comprise the substance of the subject matter (sound
conceptual understanding)
■■ Includes: Detail, including procedural and numerical aspects specific to the subject matter
■■ Excludes: Complexities and unusual / exceptional aspects
■■ Objective: Enable candidate to deal with issues and solve problems central to the topic
Level 3 – Advanced
Summary: Thorough knowledge & rigorous understanding
■■ Includes: Complexities & unusual / exceptional aspects; sufficient depth to clearly locate
content in the broader discipline & to identify implications and relationships
■■ Objective: Enable candidate to perform tasks and solve problems with a high degree of rigour,
exercising sound judgement
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OVERVIEW OF FINANCIAL
MANAGEMENT
1
You have arrived here because you are beginning your studies in finance, or you have to make a
financial decision and need principles to guide you or you may simply be curious about how the
financial world works. Finance is not a subject you study and then put away. It will have a profound
impact on your future and/or the future of your company. Developments in financial markets,
the enabling power of technology and a globalising world economy have created dramatic shifts
in financial markets and instruments. In this chapter, we will start at the beginning and explore
the objective of finance, corporate structures, the function of the financial manager, corporate
governance, sustainability and ethics. We will try to understand why management incentives may
not always be aligned with the interests of shareholders or bondholders. Did this perhaps play a role
in the global financial crisis? We will see.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Define what Financial Management is.
■■ Explain why the objective of financial management is to maximise the value of the firm.
■■ Define the role of the financial manager.
■■ Describe the various forms of business organisation.
■■ Understand how agency issues that arise between managers and owners impact on
wealth maximisation.
■■ Understand the underlying concepts of financial management.
■■ Understand what represents good corporate governance in terms of King IV.
■■ Define the role of ethics in financial decision-making and understand the codes of
conduct issued by professional accounting and finance associations.
■■ Understand the role of corporate strategy in financial management and define strategic
frameworks such as Porter’s Five Forces, SWOT and PESTEL analysis.
■■ Explain behavioural finance and how biases can affect financial decision-making.
INTRODUCTION
This text is essentially about the financial management of business enterprises. Companies
face two major financial management decisions:
■■
Which assets should the company invest
in?
■■
How should the company finance these
investments?
The first question requires that we find assets that will increase the value of the firm and the
second question requires us to raise capital – either new equity, retained earnings or debt to
finance the investment in assets. These are important financial decisions, which sometimes
mean that firms either prosper or sometimes fail. These decisions occur within a strategic
context. Corporate strategy is the compass of the firm – financial managers will make decisions
in line with a strategic vision and the core values of the firm.
The decisions required in order to ensure the growth of the business enterprise, and
therefore of the funds invested, form the core of financial management. The success of any
business enterprise depends on the strategic choices which are made and how the firm’s funds
are employed. The issues which are the focus of the financial manager relate to the sources and
uses of the funds. The criterion used to measure the effectiveness of the financial management
function is the increase in the value of the business enterprise.
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1 THE CONTEXT OF FINANCIAL MANAGEMENT
Financial management relies heavily on allied disciplines such as economics and accounting.
It is essentially an applied discipline which is approached from the perspective of the financial
manager of a business enterprise. Because of the existence of a securities exchange, a market
on which shares of companies are traded, we tend to use the listed company as the appropriate
enterprise for developing the principles of financial management. Such principles, however,
are applicable to all types of business enterprise.
Development of financial management
Individuals and organisations have been dealing in financial matters for centuries. The
development of the company form of business organisation enabled the separation of
ownership from management and ensured the continuity of business operations. The
application of limited liability to investments in companies (whereby a shareholder
cannot lose more than the shareholder’s investment in the company) enabled the pooling
of large amounts of capital to finance large business ventures. The establishment of
securities exchanges enabled investors to trade shares, and advances in technology and
information systems have enabled securities markets to react quickly to new information.
Finance theory has developed mainly since the 1950s to guide management on how to
optimise investing and financing decisions.
Links with economics
Financial management does not take place in a vacuum – it occurs in the context of a specific
national and international economy. A knowledge of the fundamental principles of economics,
and some understanding of the interaction of economic forces, is essential for the practice of
corporate finance. The financial manager should be aware of the impact of economic indicators
such as changes in the gross domestic product, the balance of payments, foreign currency
exchange rates, inflation rates, employment figures and interest rates.
Economics is the source discipline for financial management. Deeply rooted in all economic
issues is the fundamental objective of making the best use of scarce resources. In financial
management, a key resource is financial capital. The financial manager is responsible for
making the best use of this resource. This is illustrated in Figure 1.1.
Links with accounting
In South Africa, a listed company is required to produce an Integrated Report and produce
financial statements in accordance with International Financial Reporting Standards (IFRS). The
Integrated Report sets out information about a company’s strategy, its risk management policies,
governance and its management of the six capitals which are financial capital, intellectual capital,
human capital, natural capital, social and relationship capital and manufactured capital. We will
expand on this in Chapter 5. This information, together with any other relevant information, is
used by investors to place a value on the shares of the company. Accounting information has many
limitations, particularly regarding its historic perspective. Increasingly, IFRS requires or allows
assets and liabilities to be reflected at fair value (market value). Companies are also permitted to
revalue assets which were previously reported at depreciated cost in the Statement of Financial
Position. Moreover, accounting practices are designed to standardise reporting procedures rather
than to reflect economic reality. The financial manager will nevertheless be required to analyse and
interpret accounting data. This will be used in a forward-looking perspective as the information
required for financial management decisions.
The accounting profession has been criticised in recent times for its seeming inability to
develop measuring instruments, which are both reliable and relevant. This is particularly
noteworthy in the valuation of intangible assets such as research and development, brands,
patents and intellectual capital. This problem of providing information to investors and managers
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is exacerbated by the complexities of auditing large companies engaged in transactions such as
joint ventures and using a range of financing instruments such as derivatives and special purpose
entities (SPEs). These two issues present formidable challenges to the financial manager, who
needs to place reliance on information published in the financial statements of companies.
Further, fraudulent accounting practices at some major companies such as Enron, Worldcom
and Lehman Brothers caused investors to lose billions of dollars. In South Africa, the collapse
of Steinhoff due to accounting irregularities resulted in the share price falling from around
R65 in August 2017 to R1.81 in early May 2018. This represents a loss in market value to
shareholders of about R230 billion!
Economics
How do individuals/organisations/countries make the best use
of scarce resources?
Financial management
How does the financial manager use best practice to add value to capital
received in the form of debt and equity and thereby create wealth?
The financial manager
Measured by the value created by finding projects with returns that
are greater than the firm’s cost of capital.
Figure 1.1 From economics to financial management
2 THE ENVIRONMENT OF FINANCIAL MANAGEMENT
Financial management is practised in a changing business environment. Economic policies,
tax systems, inflation targets, the regulatory framework and interest rate policies adopted by
the government and the reserve bank will influence the business environment and will impact
the investment and financing decisions undertaken by companies. We need to consider these
factors before attempting to apply financial management principles within the South African
environment. What are the major forces currently shaping the South African economy?
■■ Deregulation/Regulations. Governments are increasingly removing regulations that restrict
economic activity. This has occurred in the banking sector, the telecommunications sector,
the electricity and gas sectors as well as other sectors such as the airline industry. How
will deregulation affect financial management decisions? For example, the deregulation
of shopping hours has impacted on the retail sector and will affect investment decisions
in this sector. MTN needs to consider the impact of competition and regulations in
deciding on investing in 5G. In relation to financing decisions, companies are able to
obtain financing using a wide range of instruments and from a number of sources which
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■■
■■
■■
■■
■■
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FINANCIAL MANAGEMENT
will reduce the cost of financing. At the same time, we are seeing increasing regulation of
pricing in some sectors such as electricity, water and pipelines. Bank regulation has come
under the spotlight since the financial crisis. Increasingly there are regulations arising from
competition law, labour law and environmental law.
Taxation. South Africa has undertaken major changes to the tax system which are impacting
on investment and financing decisions. The significant reduction in the corporate tax rate
from 48% to 28% in the last 25 years has affected corporate investment and financing
decisions. The implementation of a 20% withholding tax on dividends has encouraged the
use of retained earnings to finance investments in capital projects. The introduction of a
capital gains tax (CGT) which is not indexed to inflation will have long-term effects but the
lower CGT rate as well as its deferral until realisation will encourage reinvestment. South
Africa’s custom and excise taxes have been lowered resulting in an increasingly competitive
environment for South African companies. Countries have become more competitive
in terms of corporate tax rates in order to attract foreign investment. For example, the
USA reduced its corporate tax rate from about 35% down to 21% in 2018. There are
tax deductions to encourage investment in operating assets and borrowing costs are tax
deductible. There are further tax incentives to encourage research and development and
investment in manufacturing plant and equipment.
Interest rates. Interest rates have fallen significantly over the last two decades. This
means that interest rates are at low levels and this will reduce the effective cost of
borrowing and impact on the company’s investing and financing decisions. In 2018,
global interest rates were expected to rise (slowly) and South African interest rates were
expected to fall. Interest rates affect the cost of borrowing.
Inflation. Inflation has fallen significantly and companies are currently operating in a low
inflation environment. South Africa’s inflation rate is expected to stay within the range
of 3 to 6%.
Privatisation/Nationalisation. The privatisation of firms such as Telkom means that the
government has followed a policy of transferring businesses to the private sector. However,
recently there have been calls for nationalisation of sectors such as mining and the
government has begun issuing mining rights to a state mining company (AEMFC).
Commercialisation/High input costs. The South African government is committed to a
process of commercialising certain public entities such as Transnet and Eskom. The
focus is on making the public sector more efficient. However, higher electricity tariffs are
increasing the costs of doing business in South Africa.
Broad-based BEE. The implementation of Broad-based Black Economic Empowerment
is leading to changes in corporate ownership structures, management profiles,
employment, procurement policies and financing structures. The effect of BEE is
generally seen as positive for the South African economy.
Globalisation and internationalisation. Globalisation has forced South African companies
to be internationally competitive and South African companies have expanded into
foreign markets and have obtained listings in London and New York. Companies are
also raising loans and issuing bonds offshore. Tariffs may impact global trade.
Mergers and acquisitions. Increasingly we are seeing firms merging and there is increasing
consolidation in many sectors. For example, the acquisition of SABMiller by AB InBev
resulted in the world’s largest brewer.
Currency exchange rates. Foreign exchange rates are highly volatile and companies are
required to factor in future exchange rate movements in their investment and financing
decisions. The significant fall in the rand exchange rate from the beginning of 2011
($1=R6.70) to the beginning of 2016 ($1 = R15.50) and its subsequent appreciation to
about R11.80 in February 2018 and then fall (25 June 2018: $1=13.47) had significant
effects on importers, exporters, as well as local and foreign investors.
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■■
■■
■■
■■
■■
■■
1-5
Growth in the use of financial derivatives. The availability of futures, forward contracts
and options means that firms can use such instruments to hedge against price, interest
rate, currency and commodity price risks. However, the use of derivatives can result in
substantial losses when used for speculative purposes.
Developments in China, the USA and Europe. China’s burgeoning economy has resulted
in strong demand for resources and other exports from South Africa. At the same time,
local manufacturers are feeling the heat of competition from China. The continued
strong performance of the Chinese economy is crucial for exporters. It is expected that
the growth rate in China will fall over time. The USA has been incurring fiscal deficits
and undertaking “quantitative easing” by buying bonds in the market, which increases
the money supply and further reduces interest rates. This is not sustainable in the long
term. However, discontinuing this policy may have effects for emerging markets. A
debt crisis in the Euro zone a few years ago resulted in austerity and yet countries such
as Ireland, Spain and Portugal have rebounded and the Euro zone is experiencing real
economic growth and falling unemployment. The UK, due to Brexit, is experiencing
economic headwinds with higher inflation and a weak economic outlook. The USA has
experienced strong economic growth since 2009. At the time of writing in 2018, there is
real concern that there may be a trade war between the USA and China and between
the USA and Europe, Japan and Canada which may impact on world trade. There is
concern that the rising debt levels in the USA may not be sustainable. Furthermore,
interest rates were pointing to a possible recession in 2020 or 2021 in the USA. China
and Japan have high debt levels to GDP and generally the levels of indebtedness in the
world are at historically high levels.
Sovereign credit ratings. S&P downgraded South Africa to below investment grade
(“junk”) status in 2017, whilst Moody’s placed South Africa on review for a downgrade.
Yet by March 2018, Moody’s retained South Africa’s credit rating at investment grade.
Ratings are important as they impact on the interest rate payable by government and
the interest rate payable by companies on borrowings.
Economic developments in Africa. The vast economic potential of Africa, an improving
macro-economic outlook, structural changes and reforms and real economic growth will
provide opportunities for South African firms. The proposed continental free trade area
will mean that South African firms are expected to have access to a market of 1.7 billion
people with the spending power of $6.7 trillion by 2030 [Brookings Institute, 14 March,
2018]. The Harvard Business Review pointed to Africa as the next growth market and
many African economies have experienced high growth rates, although there has been
volatility.
Business disruption. Companies are increasingly subject to disruption and business
models may quickly come under pressure or even become obsolete. We can see what
Amazon is doing to retailers, how Airbnb is impacting the hotel sector, how Uber is
affecting taxi operators and what Netflix has done to videos and demand for DStv.
WhatsApp is impacting significantly on the mix of revenues of mobile telephone
companies with the rise in the demand of data not offsetting the losses from customers
no longer making traditional mobile calls. In the near future, 3-D printing, AI and
electric vehicles will become commonplace.
Demographics. The aging of the population in Europe, parts of Asia, the USA and
Australia is causing shifts in demand patterns for products and has implications for public
spending. Japan could lose about 30% of its population due to aging by 2050. Africa’s
population in contrast was 366m in 1970 and is expected to grow to 1.7 billion by 2030.
The growth in the middle class in Africa is another factor in making Africa an important
market for companies in the future.
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Climate Change. The effects of climate change are becoming increasingly relevant and
will impact on financial decisions, operating costs and demand for a firm’s products.
Where a firm locates a factory will be affected by access to resources such as water.
Forms of business organisations
Business entities can be classified in many different ways. One classification method is in terms
of the activity of the business. Using this system we can identify four main areas of activity:
Firstly, extractive activities such as mining and agriculture which form an important sector of
the South African economy. Secondly, manufacturing activities which involve the production
of goods using raw materials. Thirdly, the merchandising activities of wholesalers and retailers.
Finally, service activities which include a broad spectrum starting with government and
administrative services right through to professional services such as those provided by banks,
insurance companies, health care services, lawyers, and accountants.
From the viewpoint of financial management, however, it is also relevant to classify
activities in terms of their form of ownership. The form of ownership has numerous legal and
tax implications that affect financial management decisions. We will focus only on the common
forms of ownership encountered in business entities which have the objective of making a
profit. These are the sole proprietorship, the partnership, and the limited liability company.
Figure 1.2 Forms of business ownership
The sole proprietorship
This is probably the most common form of business entity. Anyone conducting any legal form
of business activity may be established as a sole proprietor. For tax purposes, the income of
the business is considered to be personal income of the owner and is added to whatever other
assessable income may have been earned during any given tax year. Three major disadvantages
of this form of ownership are immediately apparent. Firstly, the continued existence of the
business depends on one person, the owner. Secondly, because most individuals have limited
funds available, growth is often hampered by the inability to raise further finance. Thirdly,
should the business fail, the owner’s liability is not limited, so there is a risk that his or her
personal estate may be declared insolvent.
The partnership
A partnership may be formed when two or more persons come together to start a business.
From an individual partner’s viewpoint it is identical in every respect to a sole proprietorship,
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except that profits and losses are divided in an agreed proportion. A partnership has the
advantage of a pooling of the resources that each individual partner may be able to contribute.
These include contributions such as financial resources, technical skills, and management
expertise. There is usually a partnership agreement which will set out the responsibilities of
each partner and how each partner will share in the profits of the business.
From a legal perspective, partners are jointly and severally liable for the debts of the
partnership. This is a significant disadvantage as it means that each partner is responsible for
the actions and consequent debts of all other partners.
The close corporation
A close corporation may be formed by between one and ten persons who are referred to as
members. Members each have a proportional interest in the business. Unlike a partnership,
the interest of a member may be sold without terminating the existence of the business.
A close corporation is taxed as an entity apart from the members. Members of a close
corporation enjoy limited liability unless they conduct themselves in a way which can be
proved to be reckless or fraudulent. In terms of the Companies Act of 2008, no further
registrations of close corporations will be permitted, although current close corporations
will be allowed to remain in place.
The company
The company is a separate legal entity from the owners and is governed by the Companies
Act. This means that a company is legally like any other person and can buy, sell and transact
in its own name. It can enter into contracts and raise finance, is required to pay tax and has
the same rights and responsibilities as a natural person. The owners of the company are
called shareholders, as ownership is represented by shares of a company. As the company is
a separate legal entity apart from the shareholders, it means that shareholders have limited
liability. This means that shareholders are only at risk up to what they have invested in the
company. If a company fails, then the creditors cannot look to the personal assets of the
shareholders. This will encourage investment and enable companies to raise large amounts
of capital and enables shareholders to effectively diversify their investments. In a sense it
creates an option-like scenario, gains are unlimited and losses are limited to the amount
invested in a particular company. However, creditors are required to undertake additional
risk and may require that shareholders of smaller companies sign personal sureties. The
word Limited (Ltd) must appear in the name of the company to warn creditors that they
have the right only to the assets of the company and not to any of the shareholders’ personal
assets.
There are two main types of companies, a private company which has to include the
words Proprietary Limited or (Pty) Ltd after its name, and a public company which will
have only the word Limited or Ltd after its name. Public companies may have their shares
listed on a stock exchange such as the JSE Securities Exchange and these companies have to
comply with the listing requirements of the JSE. The shares of public companies are freely
transferable and if listed, shareholders can freely buy and sell shares on the JSE. There are
about 400 listed companies in South Africa. Private companies often have restrictions on the
transfer of shares. A private company’s Memorandum of Incorporation (MOI) is required
to state that it is not permitted to issue shares to the public. Not all corporate entities have
limited liability. A personal liability company (Inc.) is a company whereby the directors and
past directors are jointly and severally liable, together with the company, for any debts and
liabilities of the company. However, we will not focus on this type of entity.
The use of the company entity form enables the separation of management from
ownership. The shareholders will elect a board of directors who will then appoint a
management team. A number of directors will usually be involved, as executive directors,
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in the daily management of the affairs of the company. There will be a chairperson of the
board, but day-to-day management will often be the responsibility of the Chief Executive
Officer (CEO). Although the separation of management and ownership enables the
company to raise large amounts of finance, it does have certain drawbacks. For example,
how do we know that management is motivated to follow the interests of the shareholders?
But more about that later. A company’s lifespan is not limited by the life-span of its
owners. It has continuity of existence unless, of course the company fails.
Although limited liability has enabled the expansion of companies, it has also been
misused by investors who hide behind the “corporate veil”. Increasingly, the law is shifting
responsibility to the directors of the company. For example, directors become personally
liable if they permit the company to trade whilst insolvent, that is where the company’s
liabilities exceed its assets.
How many shareholders are there in a company? It depends. A private company is required
to have at least one shareholder and the company is required to have at least one director.
However, it is true to say that many private companies have a few shareholders. A public
company has to have a minimum of 3 directors and the number of actual shareholders can run
into hundreds of thousands or more. Let’s look at a few listed public companies. In 2018, MTN
had close to 125 000 shareholders whilst Vodacom had 53 529 shareholders in 2017. Pioneer
Foods had 7 365 shareholders in 2017. York Timber had 1 394 shareholders in 2017. How
many corporate entities exist in South Africa? A few years ago, the DTI indicated that there
were close to 1.3m close corporations, 400 000 private companies and close to 3 800 public
companies in South Africa.
Table 1.1 summarises the differences between the various forms of business organisations.
Table 1.1 Features of business entities
Taxation
Taxation is a significant cost to business. Tax laws are complex and constitute a separate and
specialised field of study. However, it is important to understand certain basic tax principles that
affect the daily decisions made in a business enterprise. These are considered briefly below.
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Taxation of company profits
Company profits, reported in the income statement as “net profit” for the year, are not the
complete basis for taxation. However, many accounting policies will have tax implications. A
company is liable for taxation on its “taxable income”. The “taxable income”, in turn, depends
upon the revenue or turnover which is liable for taxation and the expenses which may be deducted
from such revenue in accordance with the current tax legislation. Revenue from sales would, for
example, normally be taxable. Similarly, certain expenses such as salaries will reduce the taxable
or assessable amount. However, some expenses may be deemed to be of a capital nature and
thus be disallowed for income tax purposes. Depreciation allowances may be different from
the amounts written off by the company as depreciation, for the purposes of determining “net
profit” in the income statement. The corporate tax rate in South Africa in 2018/19 is 28%. Small
business corporations may qualify to pay a lower tax rate on income up to R550 000 in 2018/19.
The corporate tax rate has fallen significantly over the last 30 years. For example, in 1990, the
corporate tax rate was 50%.
Assessed tax losses
A company is permitted, subject to certain conditions, to carry forward to future years any losses
incurred in the normal course of business in prior years. This is of value as this will result in
future tax savings if the company returns to profitability.
Capital gains tax
Individuals and companies are subject to capital gains tax, which represents a tax on gains made
on long term assets. For example, assume XYZ Ltd acquires a building at a cost of R70m and
sells this building for R130m five years later. The company declares a capital gain of R60m, but
(in terms of tax legislation in 2018/19), only 80% of this gain is subject to capital gains tax (CGT)
at the corporate tax rate of 28% and so the company would pay CGT of R13.44m (R60m 
80%  28%). For an individual, only 40% of capital gains are taxable. So, if you as an individual
bought 1 000 shares in Woolworths for R65 per share and sold it for R105 per share three years
later, then there is a gain of R40 000 but only R16 000 is taxable at your personal tax rate.
Individual taxation
Individual tax rates operate on a sliding scale. The highest marginal tax rate for individuals is
45% and the lowest tax rate is 18%. Individuals also qualify for tax rebates, meaning that the
18% tax rate will only effectively apply above a minimum income level. Individuals are subject
to capital gains tax on the sale of assets and individual shareholders are required to pay a final
dividend tax of 20% on dividends received in the form of a dividend withholding tax.
Dividend withholding tax
South Africa moved to a dividend withholding tax of 20% which is a tax on shareholders.
The move to a dividend withholding tax system means that a company will withhold 20%
of dividends payable to shareholders but this represents a tax on the shareholders. If the
shareholder is a South African resident company, then the dividend withholding tax will not
apply and such companies will be exempt from dividend tax.
If a company pays all its after-tax profits as dividends, then the following represents the
effective tax rate for every R100 of income, if we include the dividend withholding tax:
Effective tax rate = [R28 + 20% × R72]/R100 = 42.4%
In Financial Management we focus on the effects of corporate tax as investors will face varying
personal tax rates. We will generally assume that dividend tax is not a corporate tax. This is
also due to the interaction of capital gains tax and dividend tax. Surveys of practice indicate
that companies use the corporate tax rate in accounting for tax in financing and investment
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decisions. Changes in the tax system can have a considerable impact on financial management.
Financial managers therefore need to keep up to date with changes in tax legislation.
3 WHAT IS THE FUNDAMENTAL OBJECTIVE OF FINANCIAL MANAGEMENT?
The objective of financial management is to maximise the value of the firm. We can convert this
into the objective of maximising shareholder value. If markets are efficient then this translates
into maximising the company’s share price. Why is this relevant? Management will use this
core objective to frame decision-making. Every investment or financing decision should be
preceded by the question – does this lead to an increase in shareholder value?
How does this relate to ethics, corporate governance and the roles of other stakeholders
such as employees, government, the community, suppliers and customers? The objective of
shareholder value maximisation does not have to be in conflict with ethical decision-making
and effective corporate governance. Further, a firm should consider the impact of its decisions
on the firm’s other stakeholders. A company that continues to drive down the cost of its inputs
by placing increasing pressure on its suppliers may find that its suppliers will either go out of
business or will reduce the quality of their products in order to achieve lower prices. This may
not be in the interests of the company in the longer term. The quality of the firm’s products
may be dependent on the quality of its inputs and so this policy may impact negatively on its
own value. We will come back some of these issues later in the chapter.
Is shareholder value relevant in the real world? BHP, which is one of the world’s leading
resources groups, states the following;
We have a world-class portfolio of growth options that will ensure we are able to plan for the
short and long term and continue to create value for our shareholders.
Companies may focus on corporate profitability or growth in sales and although these may be
aligned with shareholder value, these measures are at best incomplete and may lead to poor
decision-making. For example, a focus on growth could lead the company to destroy value. We
will come back to this issue later in the book. For now, we will analyse the limitations with the
objective of profit maximisation.
Why is profit maximisation not the right objective for corporate finance?
Company profitability is important for shareholders and management. We often hear of
company management being focused on maximising profits. However, it is only part of the
story and it is not a well-thought out objective. Why?
Manipulation of accounting profits
Management may be able to increase this year’s profits by reducing such costs as advertising,
research and development, and replacement of plant and equipment. However, how would
investors react if a pharmaceutical company such as Merck or an IT company such as Intel
indicated it was reducing research and development costs? The reduction in costs would
increase this year’s profits but detrimentally affect future profits. A company can reduce
the current depreciation expense by not investing in new plant equipment but eventually
this will translate to the company becoming increasingly uncompetitive in terms of quality
and price.
Management may decide to maximise accounting profits by retaining profits and reinvesting
in projects which only offer low returns on investment. Although accounting profits will
increase, shareholders would have been able to reinvest the dividends to earn a higher return
in their own names.
Accounting profits are dependent on accounting policies and management may select policies
that may not reflect economic reality. For example, when is a sale recognised? What is the life of
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depreciable assets? When is a cost an expense and when is it an asset? These offer management
flexibility in selecting accounting policies that may bolster profits in the short term.
Timing
Profit maximisation does not directly factor in the time value of money. A project that results
in a total profit of R20m per year for 5 years would be preferred to a project that generates
R10m per year for 10 years. Why? Profits that are received sooner can be reinvested to earn
higher future returns.
Cash flows
Accounting profits do not always reflect cash flows. Profits are determined by the company’s
accounting policies, whilst corporate finance is focused on cash flows.
Accounting profits and the cost of capital
Accounting profits do not include an adjustment for the cost of equity financing. In practice,
accounting profits are often reported in terms of the company’s earnings per share (EPS). This is
determined by dividing the company’s net profit by the number of shares issued by the company.
For example, a company may disclose accounting profits of R100m and if the number of shares in
issue is 40m, then the EPS of the company will be R2.50 per share. Management may be focused
on growth in EPS, but this may be the wrong objective, as was shown with Enron, but more
about that later. The important issue is that accounting profits only reflect actual costs and not
opportunity costs. An important opportunity cost is the cost of shareholders funds or the cost of
equity which is not taken into account in determining accounting profit.
Risk
Profit maximisation ignores the impact of risk on value. Shareholders will prefer less risk and
will value a company not only in terms of its future cash flows, but also in terms of the risk of
those cash flows. For example, the risk of future cash flows of Pioneer Foods will be lower than
the future cash flows of Harmony Gold. Investors will adjust for risk in determining future cash
flows. This means that an investment that promises an increase in accounting profits but also
an increase in risk may actually result in a fall in the value of the company.
Shareholders want management to maximise value
What is an appropriate objective for management to follow? It should be able to encompass all
that has been mentioned before. Shareholders want management to maximise the value of the
firm, which really means that in the long term, management should maximise the value of the
shareholders’ interest in the company. In most cases this is measured by maximising the value
of the share price. What effect will a decision have on the value of the firm? This question
should guide the actions of management. Increasingly in line with developments in corporate
governance and King IV, management are considering the interests of all stakeholders, in
order to ensure the long-term sustainability of the firm. We will come back to this later on.
Focus of financial management on decision-making
Financial management focuses on principles of decision-making. As decisions require that
estimations be made, there are few exact solutions applicable to any financial management
problem. Decisions are made on the basis of the information available at the time. With
hindsight, such decisions may prove to have been less than optimal. However, it must be
constantly borne in mind that decision-making requires acting without perfect knowledge of
the outcome.
The two variables on which financial management focuses as the primary input in decisionmaking are expected return and perceived risk. In the text we will concentrate initially on return
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and then lead into evaluating, measuring and adjusting for risk. Once again, information
systems and programs such as Excel greatly enhance the ability of the financial manager to
cope with large volumes of data, set up financial models and test the sensitivity of the expected
outcome to deviations from estimates.
If we accept that the objective of corporate finance is to maximise the value of the firm, then
we need to determine how this is achievable. Firstly management needs to make investments
that offer a return that exceeds the cost of capital, i.e. the cost of financing. Secondly, the cost
of capital will take into account the underlying risk of the company’s investments. Thirdly,
the value of the firm will be increased by the company being able to reduce its cost of capital.
For example, a company such as BHP decided to reduce the cost of loan finance by issuing
debt securities directly in the capital markets, rather than using financing from the banks which
involves a higher interest rate.
Figure 1.3 Maximising the value of the firm
Economic Value Added (EVA)
We can calculate a company’s EVA to determine whether the company has added value over
a period by comparing a company’s return on invested capital to its cost of financing (cost of
capital). This means that we deduct the cost of financing from the company’s after-tax operating
profit. In relation to the future, the calculation of EVA corresponds to the determination of
a project’s net present value, which we will describe later. We can also determine the EVA
of a company over a period such as a financial year. For example, assume that a company
has reported operating profits of R70m after tax. If the company’s investment amounts to
R600m and its after-tax cost of financing is 9%, then the company’s EVA will be determined
as follows:
Table 1.2 Determination of EVA
We can see that if the company had reported an accounting profit of R50m for the year, then
the company’s EVA would have been a negative R4m and the company would have destroyed
shareholder value for that year.
Let’s go back to Enron, a company that was “laser focused on earnings per share” and was
until its demise one of the most admired companies in the USA. The collapse of Enron cost
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its shareholders billions of US dollars. Enron prior to its collapse was reporting an accounting
operating profit of $2.4 billion whilst at the same time its EVA was negative at almost –$1
billion.
At the annual general meeting of Steinhoff in April 2018, it was disclosed that Steinhoff
had overstated its income and assets in its annual financial statements prior to the collapse of
its share price set out in Figure 1.4. Steinhoff’s reported operating profit for 2016 was €1 793m
which we roughly estimate would result in a negative EVA if we use a cost of capital above
7.5% but this is based on overstated income and asset numbers. Steinhoff’s shareholders have
paid a heavy price for the accounting irregularities and profit manipulation.
Figure 1.4 Steinhoff share price movement, 10 April 2015 to 9 April 2018
What about the ethics of maximising value?
This is a difficult question and we need to separate the honest and hardworking managers from
the rogues. There is nothing wrong in the objective of maximising value. What may be wrong is
how this is achieved. For example, to reduce costs a company may make use of child labour to
manufacture goods in a developing country. Increasingly, companies face reputational risk from
following such practices and this may reduce the value of the company’s brand. Unfortunately
the corporate landscape is littered with unethical practices by a number of companies. We believe
that ethical standards are fundamental in corporate finance and make sense in the longer term.
Companies that follow blatantly unethical practices will not survive. How is it possible to transact
in business without trust? Financial managers should focus on the interests of the shareholders
but should act in a responsible way.
In line with King IV, a company is also required to consider the interests of society, and the
environment to ensure that the firm has a sustainable future. We will come back to this later in
the chapter.
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4 THE ROLE OF THE FINANCIAL MANAGER
Having placed the environment and objectives of financial management into perspective, we
turn to the role of the financial manager. In many companies, the Chief Financial Officer (CFO)
represents the position of financial manager. However, the Chief Executive Officer (CEO) and
the Executive team will often be involved in financial decision-making and so we will stay with
the general term of “financial manager”. A pertinent question to pose is, “what does the financial
manager do?” Once we have determined what the role of the financial manager is, the text will
explore the principles and theories which are commonly used for effective financial management.
Two primary roles are performed by the financial manager. The first of these is to pursue wealthcreating investment opportunities, and the second is to find funds to finance the investments. This is
illustrated in Figure 1.5 and further explained in this section.
Operating Assets
#Non current
#Current
Explores investment
opportunities and
makes investment
decisions
Capital Markets
#Equity
#Debt
FINANCIAL
MANAGER
Financial Assets
Explores financing
opportunities and
makes financing
decisions
Money Markets
Figure 1.5 The role of the financial manager
Opportunities to create wealth
The first role of the financial manager is to explore investment opportunities within the context
of the type of business operation in which the company is engaged. Such opportunities are
then evaluated in order to establish whether they are profitable by determining whether they
are likely to increase the value of the business. Needless to say, there are often numerous
possible opportunities available from which to select. The financial manager is required to
evaluate the possibilities and rank them in order of potential profitability.
This may seem to be a relatively straightforward procedure. However, when it is considered
that such evaluation is based on predicted outcomes and that different opportunities have
different levels of risk attached to them, it becomes apparent that selection from among competing
investment opportunities requires consideration of many interacting factors. Investment
opportunities can be broadly classified into two categories, namely investment in operating assets
and investment in financial assets.
Investment in operating assets
An operating asset is any form of tangible or intangible asset bought with a view to its returning
a profit. So, for example, a manufacturing firm may consider buying plant and equipment as
operating assets. This investment would be undertaken to produce a product which, when sold,
would cover all costs related to the machine as well as material and labour costs. In addition,
some profit must be realised in order to compensate the investment in the operating asset.
Making the decision to invest in such an operating asset requires numerous estimations to
be made. These would depend on factors such as the saleability of the product and the costs
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which are likely to be incurred. The financial manager is required to collect and evaluate such
information, make estimations about cash flows related to the project, and decide whether the
investment should be made or not.
This example can be generalised to virtually every decision by a company to spend money
on assets. A company decision to buy vehicles, equipment, additional warehouses and even
considerations relating to buying inventory, are all investment decisions which are central in the
day-to-day functioning of the financial manager. For the purpose of classification, a distinction is
usually drawn between non-current and current assets.
■■ Non-current assets. From the financial management perspective, some assets are acquired in
order to produce goods or services which will be sold by the business. They include property,
buildings, machinery, equipment, and vehicles. Increasingly, intangible assets such as brands
and patents are becoming important in order to generate cash flows. For example, the
licence fees paid by MTN to acquire 3G or 4G LTE spectrum allocations are probably more
critical for its future cash flows than the cost of its base stations, towers and transmission
equipment. The intention of acquiring such assets will be to generate future cash flows which
will more than compensate for the outlay of funds for acquisition. As non-current assets
usually have a long-term use, they are usually funded from long-term sources of funds.
■■ Working capital. Inevitably, non-current assets require supporting current assets in order
to complete the operating cycle. An inventory of the goods produced must be kept on hand
in order to make them readily available to consumers. Consumers may be allowed to delay
payment, resulting in accounts receivable, a current asset. Cash must also be kept readily
available in the form of bank balances or funds available on short call. These three items,
inventory, accounts receivable, and cash, form the core of the current assets or working capital
of the business. Fortunately, investors do not usually have to finance all the current assets, as
creditors allow delayed payment for supplies to the business. The net amount, current assets
less current liabilities, is referred to as the net working capital of the business.
Investment in financial assets
What are financial assets? The investment in equity shares, preference shares and bonds as well
as other financial instruments such as derivatives and money market investments are classified
as financial assets.
As a company grows, it faces the option of acquiring additional operating assets, or
purchasing an interest in an existing operation through the purchase of the shares of a company
already in operation. This may be achieved with a view to expanding its investment in the present
business operation, or by purchasing the shares of another company already engaged in business
operations which may be in the same or a different type of industry.
The financial manager must be capable of placing a value on financial assets in order to
make decisions about such assets. As with operating assets, this type of valuation requires the
prediction of numerous variables.
Of equal importance to the financial manager is the value that potential investors place on
the company’s shares. As a high value is usually associated with maximising the value of the
company, it is important for the financial manager to understand the factors that result in the
company’s optimal value.
The valuing of financial assets is facilitated by capital markets. The JSE, for example, lists the
trading prices of the shares of about 400 companies. If the market is functioning efficiently, the
listed prices will tend to be real economic indicators of value. As they represent the aggregate of
all information brought to bear by the market participants, they reflect the price set by forces of
supply and demand for any particular share, based on all public information about the company.
Selecting the optimal finance mix
Having identified investment opportunities with wealth-creating potential, the second major role
of the financial manager is to raise funds in order to finance the investment. These two primary
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functions are not neatly ordered. The financial manager is constantly looking for investment
opportunities and constantly making decisions regarding the source of funds to be used in order
to finance the investment projects.
The objective, when canvassing financing alternatives, would be to obtain funds at the
lowest cost. The cost of finance from the viewpoint of the investor will usually be determined
by the risk which is seen to be associated with the investment. This in turn depends on the type
of projects being undertaken, the length of time for which the funds are provided, and the legal
standing of the finance in the event of liquidation of the company. Finance is usually obtained
in one of four ways – by going to the capital markets and attracting long-term finance, by
making use of suppliers’ credit, by going to the money markets and using short-term finance,
or by retaining profits which could otherwise be paid to shareholders in the form of dividends.
Finance from capital markets
Capital markets are markets in which long-term financing instruments are bought and sold.
The financial manager of a growing company is likely to be trying to acquire finance or, stated
differently, to be selling financial assets. We have been referring to investors generically up to
this point. Investors, however, all have different attitudes toward risk. Those who are prepared
to assume higher risk – with an expected high return – will prefer to acquire shares. Those who
are more risk-averse will prefer to purchase bonds which are more secure and invest in loans
secured against fixed property. Investment opportunities, from the perspective of individual
investors, can therefore be broadly categorised into shares or debt, in return for which they
offer their cash.
■■ Issue of shares. If a company raises long-term capital by issuing shares, ordinary
shareholders face the ultimate risk in that they will be the last to be repaid in the event of
liquidation. For this reason share capital is relatively expensive. Shareholders expect a high
return for the risk which they take. Shares may be packaged in different forms in order to
reduce the risk for some categories of shareholders. So, for example, shares of a certain type
may give the holder a preference payment of dividends and in some instances preference in
the event of liquidation. Ordinary shares, bear the highest risk, but also gain the most benefit
if a company is profitable and shows growth.
■■ Issue of debt. A company may go to the capital market in order to raise long-term debt.
Once again there are numerous forms of debt which could be issued. These range from
debentures or bonds, which may be secured by mortgage over immovable property or be
convertible into shares, to term loans at fixed interest rates or rates fluctuating with a base
rate such as the prime rate or JIBAR. Increasingly capital markets such as the JSE have
electronic trading systems in place. For example, it is possible to trade corporate bonds and
shares on the JSE. Markets for other long-term debt are usually created by investment banks
and other financial institutions which place long-term debt with companies for their clients.
These markets may have no specific location, but operate as a result of negotiation between
parties, often initiated by telephone.
Finance from money markets
Money markets play an essential role in satisfying short-term financing needs. This need arises
most frequently as a result of the cyclical or seasonal nature of many businesses. It would be an
unnecessary waste of resources to borrow funds for a long term and then keep them idle for a
large part of each year.
The money market creates the opportunity for short-term borrowings and short-term
investments of surplus cash. A bank overdraft facility is an example of a short-term borrowing,
which is normally renegotiated with the bank every year.
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Finance from creditors
A large component of current assets often comprises goods purchased from suppliers. The extent
to which suppliers offer credit terms will determine their contribution to the financing of working
capital.
Finance from retained income
A fourth method of obtaining finance is by retaining part of the company’s profits each year.
How much of the net earnings should a firm retain and how much should the firm pay as a
dividend? If the firm has highly profitable projects, then it should retain all its current profits
to invest in these projects. Yet, it is also true that if a company decides to cut its dividend,
this may cause its share price to fall. In Chapter 16, we will study a number of dividend
theories, in regard to the effect that the dividend decision can have on the value of the firm.
The interaction of investment and financing decisions
The interaction of investment and financing decisions is evident from the Statement of
Financial Position of a company.
Figure 1.6 illustrates the Statement of Financial Position of Vodacom in a way which
highlights the distinction between the investment and the financing decisions. The investment
in assets equals the total financing provided by shareholders and debt holders. Some of the
providers of finance (shareholders and long-term debt providers) require a return on their
funds. Under current liabilities, trade and payables (mainly creditors) do not earn a return
in the same way (dividends or interest). This is because their return is already built into the
price of the goods purchased by the business.
The equity and non-current liabilities sections of the Statement of Financial Position,
reflects the claims by long-term investors in equity and debt against the assets of the business.
The business must operate in such a way as to generate an adequate return to all suppliers
of capital. Failure to do this will result in disinvestment and the consequent deterioration
of the business and its future prospects. The financial manager is therefore engaged in a
dynamic strategy of investigating investment opportunities that correspond with the business
objectives and ensuring that the optimal mix of equity, debt, and creditors is being used to
finance the profitable opportunities.
Vodacom, which is majority owned by Vodafone, provides voice, messaging and data
services to about 74m subscribers, mainly in South Africa but also in other African countries.
Vodacom has invested in assets such as base stations and licences and uses borrowings and
equity capital such as retained earnings to finance its assets.
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Figure 1.6 Statement of Financial Position of Vodacom, showing investment and financing decisions
Figures 1.7 and 1.8 illustrate the interaction between the financing and investing activities of a
hypothetical business, using financial statements to illustrate the returns, assets and financial
claims on those assets.
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Figure 1.7 Statement of Comprehensive Income
Figure 1.8 Statement of Financial Position
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FROM THE REAL WORLD
BHP is a leading global resources company with sales revenue in 2017 of US$38.3 billion,
operating profit of US$11.75 billion and net profit of US$6.2 billion. The company has about
60 000 employees and contractors and operates globally. The company is a major producer of
iron ore, coal, oil and gas, copper, nickel and potash. BHP is focused on maximising shareholder
value and the company’s 2017 Annual Report makes numerous references to this objective. The
company states the following:
Our corporate purpose is to create long-term shareholder value through the discovery, acquisition,
development and marketing of natural resources. We do this through our strategy: to own and operate
large, long-life, low-cost, expandable, upstream assets diversified by commodity, geography and market.
The Board sets the long-term strategy for BHP, considering all our opportunities for the creation of
long-term shareholder value. The Board has the experience and skills to assist the Group in the optimal
allocation of financial, capital and human resources for the creation of long-term shareholder value.
It also means the Board understands the importance of meeting the expectations of stakeholders,
including in respect of the natural environment. Identifying and managing risk and opportunity are
central to achieving our corporate purpose of creating long-term shareholder value.
BHP has implemented remuneration incentives to align senior executive rewards with long-term
sustainable shareholder value creation.
Pioneer Foods is a leading company in the food and beverage sectors. Its main divisions include
Sasko, Bokomo Foods, Ceres Beverages and its stake in Heinz Foods. Sales revenue amounted
to R19.6 billion in 2017. The company states the following in its 2017 Integrated Report:
The Group is equally compelled to increase long-term shareholder, as well as social, value. Creating
shared value for all stakeholders is a priority for Pioneer Foods.
The integrated report of Pioneer Foods indicates that for the calculation of Economic Profit,
“applicable EBIT will be tax adjusted and compared to the Group’s WACC for the year as
applied to the average net asset base”. This is very similar to EVA.
Pioneer states in relation to its executive long-term incentive remuneration policy, that “no
value (for management) is realised unless the share price increases over the performance period.
This creates true shareholder alignment.”
Shoprite states that its executive remuneration policy provides “employees with an opportunity
to own Shoprite shares which fosters a culture of ownership and alignment with shareholders”.
Truworths states in its integrated report that:
During the 2017 financial period the Group continued to practice corporate governance at a
high level, aimed at adding value to the business as well as facilitating the Group’s sustainability,
generating long-term shareholder value and benefiting other Stakeholders. The (remuneration)
committee periodically reviews the Group’s remuneration strategy to ensure it remains aligned with
the objective of enhancing shareholder value.
Vodacom indicated the following in its 2017 integrated report:
Our balance sheet remains strong, providing us with sufficient capacity for leverage,
enabling us to execute our growth strategy and realise possible M&A opportunities where
these contribute to adding shareholder value. Our long-term incentive, in the form of an
annual share allocation, encourages ownership and loyalty, and supports our objective to
retain valued employees. It is designed to align executive performance to shareholders’
interests.
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So how does this fit with our story so far? Firstly, the focus is on maximising shareholder value
subject to other stakeholder considerations. Further, risk management is central to the creation
of shareholder value. Remuneration structures are aligned to the creation of shareholder value.
Further, management is focused on maximising the value of the company by investing in
projects which generate returns above the cost of capital. This will translate over time to increases
in shareholder value. These objectives are in line with what this book is about.
5 FUNDAMENTAL CONCEPTS OF CORPORATE FINANCE
The emphasis in this text will be placed on the fundamentals essential to an understanding
of the issues and decisions that confront financial managers. All practices in financial
management, evidenced by the decisions and actions of the financial manager, are based
on underlying concepts. Of particular significance in finance is the assumption that people
will choose an investment with a higher expected return rather than a lower expected
return, all other factors being constant. Similarly, if two investments both have the same
expected return, investors acting rationally will prefer the investment with the lower risk.
We will now explain some of the key concepts in financial management.
Present Value
The present value concept enables us to determine the value today of expected future cash
flows. This means that we can compare investments with differing cash flows which will occur
at different times in the future. This concept is based on the premise that there are active
capital markets in order to determine appropriate required returns or discount rates.
Time value of money
The value of any investment is determined by both the size of the future cash flows and the
timing of the cash flows. Investors prefer to receive cash flows sooner rather than later, as
these cash flows can be reinvested to earn a return. The use of a discount rate to determine the
present value will include an adjustment to take into account the time value of money.
Risk and return
Corporate finance is based on the concept that investors will prefer low risk investments and
therefore will require higher returns from projects with higher risk. How do we measure risk?
How do we adjust for risk? These are questions we will address later in the text. For now, it
is important to understand that a company should only invest in a project that offers a return
that is in line with its level of risk. The discount rate that we use to determine the present
value should include an adjustment for risk. The Capital Asset Pricing Model is one model that
enables us to calculate a risk adjusted required return or discount rate.
When we apply a required return or discount rate to determine the present value of future
cash flows, the required return will be made up of the risk-free rate which reflects the interest
rate on government bonds, and a risk premium which includes an adjustment for risk. The riskfree rate reflects the time value of money.
Required return = Risk-free rate + Risk premium
No Arbitrage Principle
What is arbitrage? Arbitrage occurs when we buy and sell the same good in different markets
to take advantage of any price difference. If gold is trading in London for a higher price than in
Johannesburg, then we can buy gold in Johannesburg and sell gold in London. This represents
an arbitrage opportunity. A more inclusive definition states that arbitrage occurs when we are
able to make risk-free gains or when we are able to make gains with no investment. Of course,
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an arbitrage gain is possible if traders make mistakes in setting prices but we would not expect
that such price differences would persist for a long time. In corporate finance, the no arbitrage
principle is important for determining prices for commodities, bonds, derivatives and equities.
A simple example will illustrate the no arbitrage principle. Anglo-American plc is listed on
the London Stock Exchange and has a secondary listing on the JSE. Assume that it is 11.00 am
on a cold winter’s Tuesday morning in Johannesburg in July, that the share price in London is
£15 at 10.00 am (London is 1 hour behind South Africa at that time of year). The Rand-Sterling
exchange rate is R18 = £1 and Anglo-American is trading on the JSE at R300 per share at
that moment. If you are quick and there are zero transaction costs, then you will buy sterling
and then buy shares in London for an effective Rand cost of R270 (£15  18). You would sell
each share on the JSE for R300. This is risk-free arbitrage as you will buy and sell at the same
moment. If such arbitrage opportunities exist, then we would expect this not to persist for
very long. Why? Arbitrageurs would continue to buy in London and this would raise the share
price in London. As arbitrageurs continue to sell in Johannesburg, the price will fall on the
JSE so that prices will move towards each other until no further arbitrage opportunity exists.
Arbitrage opportunities occur infrequently and are quickly eliminated. Otherwise, transaction
costs or taxation may offset any potential gain. Corporate finance theory relating to capital
structure and the pricing of financial instruments and derivatives depend on this principle.
There are two types of arbitrage opportunities. Firstly, we can make a zero net investment
and be assured of a positive gain. Secondly, we can make a net investment today and be
assured of a positive gain in the future. In the first case, we may take offsetting positions in
assets simultaneously that will ensure we make a gain. The above example of buying shares in
London and selling the same shares in Johannesburg is such a case.
An example will indicate how we will make a certain profit in the future. Assume that the
current price for A Ltd is R100 per share and A Ltd does not pay a dividend. The interest rate
is 10% per year. Let’s assume that a financially strong company, B Ltd, indicates that it will
enter into contracts today to buy shares in A Ltd in a year’s time for R125. What would you
do? If this were the case then you would immediately borrow R100, buy one A Ltd share today
for R100 and enter into a contract today to deliver one share in A Ltd for R125 in one year’s
time to B Ltd.
In a year’s time, you deliver the share to B Ltd and you receive the sales proceeds of
R125; you pay back the loan of R100 plus interest of R10 and make a certain profit of R15.
Therefore, we do not expect that this would happen very often and so we can estimate that the
forward price is expected to be R110 as then there is no incentive for arbitrage. Another way
of explaining the no arbitrage principle is that there is no free lunch! Remember that if assets
result in the same cash flows or pay-offs, then the values of these assets should be equal.
Efficient markets
The efficient markets hypothesis (EMH) postulates that securities markets react immediately
and without bias to all new information. The EMH assumes that prices fully reflect all available
information. If the EMH actually applies in practice, then it is impossible for any investor to
earn a consistent return in excess of the return warranted by the risk class of the investment.
Stated more simply, any “hot tips” or news about “winners” which will earn above normal
returns is out of date when heard, because the share market will already have absorbed the
information into the price. There are less rigorous levels at which this theory has been tested,
such as positing it applies only to publicly available information. Information comes to the
market in a random manner and prices react quickly to new information.
Are markets always efficient? New developments in finance indicate that markets do overreact to information and shares that do poorly in one period tend to do better in the next
period. Companies achieving very good returns in one period, tend to see a fall in returns in
a later period. This relates to a period of over three years. Investors are engaging in herd-
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like activity and there is a growing specialisation in what is now termed behavioural finance,
which we explain in Appendix 1.1. Although markets may not be viewed as perfectly efficient,
the market is reasonably efficient in compounding so much financial information into one
measure, the company’s share price.
Portfolio theory
Almost intuitively we all know the dictum that we should never place all our eggs in one basket.
This is another way of saying that if we are to behave in a rational manner, we should diversify
our investments so as to reduce our risk. Portfolio theory has explored this theme with some
implications for financial management. A feasible method of mathematically quantifying risk
and the effect of diversification was developed. More consequential, however, is the further
development of investment principles pertinent to holding share portfolios. Essentially, risk
can be reduced by the combination of assets into portfolios of shares in different sectors of
the economy.
Capital asset pricing model
The price of an asset is usually stated in terms of the required return on the asset. Such return
would clearly reflect the estimated risk of the asset. A capital asset pricing theory attempts to
measure the risk of a financial asset and to express the price in terms of the required return.
Developments which stemmed from portfolio theory led to a widely accepted theory
for pricing capital assets known as the capital asset pricing model. This model holds that a
certain level of risk applies in a market to all capital assets and must be borne by the investor,
while other risk is peculiar to the specific asset and can be eliminated through diversification.
The only risk of any significance to decision-making is therefore the risk which cannot be
eliminated. The model thus seeks to establish the impact of the undiversifiable risk, enabling
investors to establish the risk they are prepared to take from a portfolio in order to induce
them to purchase that portfolio.
The capital asset pricing model is often used in practice. Yet this model is also being
questioned and we will come back to this later in the book.
Financial analysis
Corporate finance requires an understanding of financial statements. Often, financial managers
are required to work with financial statements and understand the effect of accounting policies
or at least be able to deconstruct financial numbers to get to cash flows. Although we have
indicated the limitations of using accounting numbers, the reality is that often they will be our
first port of call. In order to determine future cash flows we can focus on financial statements
and make the necessary adjustments, such as adding back depreciation to determine a
company’s cash flows from operations.
Analysing the Statement of Financial Position indicates the decisions undertaken by
management. The level of non-current assets reflects the investment decisions of the company
and the decision of how much financing is provided by the creditors and shareholders is also
disclosed. In corporate finance we wish to optimise the investment in assets, net working
capital and financing structures that will maximise the value of the firm.
6 DO MANAGERS ACT IN THE INTEREST OF SHAREHOLDERS?
The separation of management and ownership means that the managers of many large
listed companies own a very small proportion of the shares of the company. This means that
shareholders and management have an agency relationship. In an agency relationship the
managers act as agents for the shareholders but may put their own interests first. Management
are the agents of the shareholders and should act to maximise the value of shareholders’ wealth.
Yet there is a real possibility that the shareholders as owners will experience losses because
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managers take decisions that are in the best interest of managers and are detrimental to the
interest of shareholders.
What actions may management take that may not be in the interests of the shareholders?
Management may unnecessarily acquire an expensive corporate jet; operate from gleaming
head offices with views; and incur expensive travel such as spending about R90 000 for three
days in Rome on a “business” visit. Management will be motivated to structure for themselves
overly generous remuneration plans. More serious for the wealth of shareholders is a propensity
to engage in the acquisition of companies in unrelated business areas – so called corporate
diversification and empire building.
Also, management might avoid risky but worthwhile projects as the risk to their own financial
position is high as compared to the risk of the project to well diversified shareholders. Let us
assume that Co. A and Co. B are considering undertaking oil exploration in two areas and
both have a 50% chance of striking oil. The value of the existing operations of each company
is R80m and striking or not striking oil will mean for each company, that it will either go out
of business by losing R120m or will treble its market value by adding R160m in value. Any net
loss will be financed by the firm’s shareholders. For a well diversified investor who owns equal
shareholdings in both companies, it is easy; both companies should drill for oil as the expected
value of the total investment will grow from R160m to R200m. This is shown in Table 1.3.
Table 1.3 Management and risk
For management, it is not so easy. If the company invests, there is a 50% chance that the
company will fail and management will lose their jobs and possibly their pensions. Management
may also feel a sense of loyalty to their employees and their debt holders not to place the future
of the firm at risk. Therefore in this context, management of both companies may decide not to
invest in the project. Management may also decide to use less debt than optimal, as low debt
levels mean a lower propensity for bank managers to place them under pressure.
How do shareholders ensure a closer alignment of the objectives of shareholders and
management? In order to avoid conflicts of interest, and ensure that management do not follow
their own objectives, shareholders will incur monitoring costs which will include controls and
incentives to encourage management to take decisions that maximise shareholders’ wealth.
These controls and incentives reflect agency costs. Why would management be motivated to
maximise shareholders’ wealth? There are a number of reasons.
Shareholders appoint the board of directors at the annual general meeting and the board
has the responsibility to ensure that management acts in the best interests of the shareholders.
Although the executive directors and management may have effective control of the board
of directors, the current focus on proper corporate governance and the appointment of
independent and non-executive directors mean that it is expected that this will ensure a greater
propensity by the board to change the management team if it is not acting to maximise the value
of the firm. However, management controls the flow of information to the board of directors
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and often non-executive directors are not able to spend the time required to understand fully
the complexities inherent in current business operations as well as being fully aware of the use
of complex financing instruments, such as derivatives.
It is also true that the Companies Act 2008 places greater responsibilities on the board of
directors and there are greater risks of personal liability. King IV also places greater corporate
governance requirements on all directors.
Compensation plans provide incentives that ensure an alignment of the interest of
shareholders and management. For example, the granting of share options to management, so
that management will share in any share price appreciation, means that management will be
focused on maximising the share price. It is true that management are increasingly taking
actions such as cost cutting, reducing capital investment and focusing on increasing revenue.
The performance by South African banks in the last 15 years in reducing costs and raising
revenue and the share price is partly driven by the focus on shareholder value.
The threat of take-over is real for underperforming companies as a depressed share price
often reduces the effective cost of a take-over which invariably leads to the incumbent
management team being shown the door. Ensuring a high share price means that a company
will be unattractive as a take-over target, although sometimes a strong management team may
be an incentive for the merger.
What is wrong with the theory? Although we can expect management to earn millions if
there has been a significant increase in shareholder wealth, there have been many cases where
management, particularly CEOs, have received very large payouts even when the company has
performed badly. Further, there may be very little correlation between share price movements
and executive performance. Share price movements may be driven by general economic
conditions and falling interest rates rather than by management performance.
Management incentives, share options and the financial crisis
Another issue relates to unintended consequences of management incentives. Share options
became the largest component of management remuneration. In theory, this should align the
interests of management with the interests of shareholders. In fact share options will only do
this if the options are deep in the money on issue date but this will often not be the case. Share
options can result in management being incentivised to take on higher risks than optimal from
the shareholders’ perspective. How? Let’s go through a simple example.
RM Ltd has 100 million shares in issue which are currently trading at R15 per share. The
market capitalisation of the firm is therefore R1 500m (15 × 100m). Management is issued with
10m share options whereby management has the right (not the obligation) to buy 10m shares in
the company for R15 per share. We will make this simple and will avoid time value and other
issues in option pricing for now. We will come back to these issues in Chapter 18. We will assume
that right after the issue of the options, an opportunity arises for the firm to invest in a project
that will either lose R1 000m resulting in a fall in the value of the equity in the firm to R500m or
the project may succeed resulting in a gain of R1 100m and an increase in the value of equity to
R2 750m. [R1 500m + R1 100m + R150m (proceeds from exercise of options)].
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Due to the high risk of failure, and the risk-return profile, the shareholders may prefer that the
project is not accepted. The current shareholders will either gain R1 000m or lose R1 000m. Why
did we use a gain of R1 000m for the current shareholders and not R1 100m? If the project fails,
the share price will fall to R5. The options have no value and management will not exercise their
options and so the number of shares in issue will remain at 100m shares.
If the project succeeds, then the option holders will exercise their options to buy at R15 per
share as the share price is expected to be R25 per share after the exercise of all the options.
The company will issue 10m shares in terms of the options resulting in 110m shares in issue.
Let’s evaluate the relative wealth positions of current shareholders and management if the
project fails or succeeds as follows:
For the current shareholders, they may lose R1 000m or gain R1 000m [100m × (25 – 15)].
For the management team with options, their loss is limited to zero and their gain is R100m if
the project succeeds. Management’s incentives indicate that the project should be accepted, as
they obtain a significant part of the gain whilst the shareholders would prefer not to accept this
project as they will take all losses. If the options had an exercise price of R10 and the current
share price was R15, then management would think twice about the project. This is because
they would then have something to lose. If the project fails, the options would have little value,
as the share price would then be R5.
It is true that the interests of management and shareholders are aligned in terms of the
focus on the share price. However, with share options, management may be incentivised
to accept higher risk projects. Of course, this conflict may be balanced to some extent by
management also being offered sizable salaries and a fixed remuneration. It’s a wonderful
world for management. Share options played a role in the financial crisis. Yet, it is also true
that we cannot simply blame management. It is all about creating the right incentives. You get
what you incentivise!
King IV recognised the role that share-based incentives can play and stated that participation
should be restricted to employees and executive directors. Non-executive directors should not
receive share options or other incentive awards geared to the share price. Vesting of rights
should not be less than three years. There should be no re-pricing of options that are underwater.
Another agency problem: shareholders and bondholders
When banks lend funds to a company or when investors purchase a company’s bonds, they do
so on the basis of the risk of existing assets, future assets, the level of borrowings as a percentage
of total assets and the riskiness of the company’s future cash flows. Yet management may
undertake the following actions to transfer wealth from the debtholders or bondholders to the
shareholders in the short term:
■■ Issue more debt as this will reduce the value of existing debt.
■■ Increase dividends which means that the debtholders will have less security.
■■ Increase the risk of the assets as the full benefits will flow to the shareholders whilst the
losses will be partly borne by the debtholders.
Capital markets do not forget. Whilst shareholders may reduce the value of bonds or debt,
future access to capital markets will be limited and the cost of financing will rise. Companies
are focused on maintaining good bond and debt ratings as this ensures lower cost financing in
the future. Further, lenders include loan covenants which restrict the actions of firms to transfer
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wealth from the bond holders to the shareholders. So banks will require that companies adhere
to certain net current ratios, debt ratios and dividend payment policies.
We will come back to the issue of loan covenants in Chapter 13.
7 DOING THE RIGHT THING: ETHICS IN BUSINESS AND KING IV
This book is about financial decision-making. Yet it is also true that most decisions have
an ethical dimension. Ethics should influence everything a company does and a company’s
reputation is often built on ethical values and good corporate governance. Increasingly,
reputation affects value and a company may fail simply by not applying ethics in its operations.
One can see what happened to Arthur Anderson when it lost its moral compass – but more
about that later.
King IV states that the board should ensure that the company’s ethics are managed
effectively. This involves ensuring an ethical corporate culture, articulation and adherence
to ethical standards, and implementing a code of conduct and ethics-related policies. There
should be an integration of the code of conduct with a company’s operations and the company’s
ethics performance should be assessed, monitored and disclosed.
What do ethics mean? How do we define ethics? King IV states that ethics refers to that
which is good or right. King IV states in its practices relating to ethics that the board should
focus on characteristics such as integrity, competence, responsibility, accountability, fairness
and transparency. King IV indicates that responsible corporate citizenship implies an ethical
relationship between the company and the society in which it operates. For example, Bidvest
states the following in its 2017 integrated report:
Stakeholders can only derive full value from a business founded on honesty, integrity,
accountability and respect.
Professional associations such as SAICA, ACCA, CIMA and the CFA Institute emphasise
professional ethics and a Code of Conduct for their members. We have included extracts from
SAICA’s Code of Professional Conduct and the CFA Institute’s Code of Ethics and Standards
of Professional Conduct in Appendix 1.2. We will focus now on corporate governance and the
role of King IV in South Africa.
8 CORPORATE GOVERNANCE AND KING IV
Companies play a pivotal role in the global economy, in society and often have a significant
impact on the environment. The governance of companies is arguably almost as important as
the governance of countries. We explained in a prior section the potential conflicts between
shareholders, management and bondholders. Corporate governance may play an important role
in resolving some of these conflicts.
Corporate governance deals with the relationships between management, shareholders,
directors and other stakeholders. It includes the policies, procedures, processes and controls
employed in the management of a company. It includes the checks and balances required to
reduce the potential for conflict between management and the board of directors, shareholders
and other stakeholders.
The separation of ownership and control has led to an increased focus on such issues as
management accountability, transparency and the role of the board of directors who are elected
by the shareholders of the company. Management wield a substantial amount of power in the
light of widely dispersed shareholders. In other cases, minority shareholders have little power to
influence the actions of management. The consequence of corporate scandals such as Enron,
WorldCom and Tyco, was that the USA passed the Sarbanes-Oxley Act (SOX) to ensure proper
corporate governance processes. Yet it is also true that the cost of the implementation of SOX
has superseded the cost of the corporate scandals to date and did not seem to prevent activities
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at AIG and Lehman Brothers. As De Montaigne wrote hundreds of years ago, “more laws, less
justice”.
Corporate governance should ensure that management and the board of directors act in the
interest of the shareholders, although increasingly, this includes other stakeholders. The board
should be independent of management and there should be adequate systems of internal controls
in place, good IT governance and good risk management policies in place. Management should
ensure that the company adheres to high ethical standards, acts within the law and complies with
all applicable regulations. Management should ensure that the company’s financial performance
and position, information on operations and risks are properly reported to its shareholders.
In South Africa, good Corporate Governance practice is set out in the King IV report.
The key principles of King IV relate to effective leadership, sustainability and corporate
citizenship. The board of directors should set the ethical values of the firm and define corporate
strategy. Sustainability is defined as the primary moral and economic imperative of the current
century. Corporate citizenship requires that the company should operate in a sustainable manner
and sustainability is embedded in the South African Constitution. Companies are required to
consider the social, environmental and economic impacts of their operations. King IV implies
that strategy, risk, performance and sustainability are inseparable.
The King IV Code
King IV is effective for companies with financial years beginning from 1 April 2017. This means
that companies with yearends from 31 March 2018 will be reporting on the basis of the King
IV Code. Although it is a voluntary code which should lead to effective corporate governance,
the JSE makes it mandatory for listed companies to adhere to the King IV principles and
practices. Furthermore, aspects of King IV represent statutory requirements in terms of the
Companies Act.
King IV refers to the three paradigm shifts in the corporate world:
■■ Inclusive capitalism. This means that there is a triple context to a company’s operations
– the economy, society and the environment. Inclusive capitalism requires that a
company considers its use of resources and relationships (the six capitals) to create
value. The six capitals refer to Financial Capital, Intellectual Capital, Human Capital,
Natural Capital, Social and Relationship Capital and Manufactured Capital. We will
come back to this in greater detail in Chapter 5.
■■ Long-term sustainable capital markets. Sustainability naturally involves a time dimension
and value needs to be created in a sustainable way. A company may engage in practices
that may save costs in the short term but which may create risks for the company in the
longer term. Product recalls in the food sector and pharmaceutical sectors may refer
to a short-term focus and a lack of adequate processes to reduce risks. Manufacturers
have had to recall motor vehicles due to faulty brakes, accelerators, and more recently
exploding Takata airbags (please check if your car is affected). The global financial
crisis was partly caused by short-term incentives.
■■ Integrated reporting. Although annual financial statements are critical for shareholders
and other stakeholders to evaluate a company’s financial performance and financial
position, it is not enough. Environmental, social and governance reporting has become
mandatory in some countries. Integrated reporting requires that management report
on its use of the six capitals which are interconnected and therefore requires that
management engage in integrated thinking in relation to setting strategy and making
corporate decisions. There is a focus on stakeholder engagement and stakeholder
relationships.
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What is the board’s primary governance role and responsibilities?
King IV indicates that the board steers and sets strategic direction, approves policy and planning,
oversees and monitors implementation and execution by management and ensures accountability
for performance on the basis of reporting and disclosure.
King IV defines corporate governance as the exercise of ethical and effective leadership by
the board for the purpose of achieving the outcomes set out in Figure 1.9.
Figure 1.9 Corporate governance outcomes of King IV
The King IV Code requires that a board apply and explain. It is assumed that the board will
adhere to the principles and will need to explain which practices the board has implemented in
order to achieve the governance principles set out in the Code. King IV sets out 17 principles
and 208 associated practices.
King IV refers to corporate citizenship which recognises that the company is an integral
part of society and this citizenship status confers rights, obligations and responsibilities towards
society and the natural environment. The wider definition of a “licence to operate” captures
a company’s rights and obligations to society. A company should operate within the triple
context and needs to consider the needs, interests and expectations of material stakeholders.
This goes beyond the narrow focus of shareholders.
In Part 5 of the King IV Code, the principles and practices are set out under the five
headings (five parts) as depicted in Figure 1.10. The relevant principles from 1 to 17 are
referred to within each part.
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Figure 1.10 The five parts to corporate governance and related principles
The principles are set out below. King IV refers to The Governing Body but we have inserted
The Board as we are mainly dealing with companies and groups and the relevant governing
body is the Board of Directors.
KING IV PRINCIPLES
1. The Board should lead ethically and effectively.
2. The Board should govern the ethics of the organisation in a way that supports the
establishment of an ethical culture.
3. The Board should ensure that the organisation is, and is seen to be, a responsible corporate
citizen.
4. The Board should appreciate that the organisation’s core purpose, its risks and
opportunities, strategy, business model, performance and sustainable development are all
inseparable elements of the value creation process.
5. The Board should ensure that reports issued by the organisation enable stakeholders to
make an informed assessment of the organisation’s performance and its short, medium
and long-term prospects.
6. The Board should serve as the focal point and custodian of governance in the organisation.
7. The Board should comprise the appropriate balance of knowledge, skills, experience,
diversity and independence for it to discharge its roles and responsibilities objectively and
effectively.
8. The Board should ensure that its arrangements for delegation within its own structures
promote independent judgement and assist with balance of power and the effective
discharge of its duties.
9. The Board should ensure that the evaluation of its own performance and that of its
committees, its chair and individual members supports continued improvement in its
performance and effectiveness.
10. The Board should ensure that the appointment of and delegation to management
contribute to role clarity and the effective exercise of authority and responsibilities.
11. The Board should govern risk in a way that supports the organisation in setting and
achieving its strategic objectives.
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12. The Board should govern technology and information in a way that supports the
organisation in setting and achieving its strategic objectives.
13. The Board should govern compliance with applicable laws, and adopted, non-binding
rules, codes and standards in a way that supports the organisation being an ethical and
good corporate citizen.
14. The Board should ensure that the organisation remunerates fairly, responsibly and
transparently so as to promote achievement of strategic objectives and positive outcomes
in the short, medium and long term.
15. The Board should ensure that assurance services and functions enable an effective control
environment, and that these support the integrity of information for internal decisionmaking and of the organisation’s external reports.
16. In the execution of its governance role and responsibilities, the Board should adopt a
stakeholder-inclusive approach that balances the needs, interests and expectations of
material stakeholders in the best interests of the organisation over time.
17. [applicable to institutional investors] The Board of an institutional investor should
ensure that responsible investment is practiced by the organisation to promote the good
governance and creation of value by the companies in which it invests.
It is assumed that companies have applied the principles. The Board is required to explain
which practices it has implemented in order to substantiate any claim of good corporate
governance in relation to the outcomes set out by King IV. The Code has set out 208 practices
which companies may implement in order to achieve good corporate governance.
So, what are some of these practices? We will only select a few. For example, in relation to
Principle 4 with respect to Strategy and Performance, King IV states that the board “should
ensure that it approves the policies and operational plans developed by management to give
effect to the approved strategy. These include the key performance measures and targets
for assessing the achievement of strategic objectives and positive outcomes over the short,
medium and long term.”
In relation to Principle 7 with respect to Board Composition, King IV states that the
board should; “promote diversity in its membership across a variety to attributes relevant for
promoting better decision-making and effective governance, including field of knowledge,
skills and experience as well as age, culture, race and gender.” It goes on to state that the
board should set targets for race and gender, should establish arrangements for rotation of its
members and establish a succession plan for its membership.
In relation to Principle 11 on Risk Governance, practice number 4 states that the board
“should evaluate and agree the nature and extent of the risks that the organisation should be
willing to take in pursuit of its strategic objectives”. It should set out its propensity to take
appropriate levels of risk and set “the limit of the potential loss that the organisation has
the capacity to tolerate”. The Board should exercise ongoing oversight of risk management
which should include “an assessment of the risks and opportunities from the triple context in
which the organisation operates and the capitals that the organisation uses and affects”. Risk
management is seen as one of the pillars of corporate governance. Guidelines such as ISO
31000 are useful for the effective risk management of companies.
Technology and Information has become an integral part of doing business and may create
significant risks and opportunities for companies. Principle 12 refers to Technology and
Information Governance and practices include approval of a policy setting out the direction
of the employment of technology and information as well as oversight of technology and
information management which may include arrangements to provide for business resilience,
responses to cyber-attacks and “management of the performance and risks pertaining to
third-party and outsourced service providers”. Oversight should include an assessment of the
value of investments in technology and information. Directors should evaluate expenditure
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on Technology and Information assets and should review issues such as disaster recovery
planning, adherence to laws and codes, reliance on systems, legal risk relating to technology
and use of data, privacy issues and information security.
The audit committee
In terms of the Companies Act, 2008, all listed and public companies are required to have
an audit committee. In terms of King IV, all members of the audit committee should be
non-executive independent directors. The audit committee is required to nominate the
external auditor and agree fees as well as determine the nature of non-audit services. The
audit committee is required to review the financial statements and ensure the integrity of the
integrated report, including the reliability of the reporting of sustainability issues. The audit
committee is required to oversee a risk-based internal audit.
Directors and the separation of the CEO and the chairperson functions
The majority of directors should be non-executive directors of which the majority should be
independent. It is important for the CEO and Chairperson functions to be separated. Why?
The chairperson is required to manage board meetings and assist the board of directors to
evaluate the performance of the CEO. If the CEO and the chairperson is the same person,
then it becomes much more difficult for the board to evaluate the CEO’s performance, set
the CEO’s remuneration and, if required, to fire the CEO. Effectively, the CEO would be
evaluating himself and let’s face it is unlikely to be an objective assessment. It is important to
have a strong independent chairperson. Management should not create incentives that reward
short-term profits at the cost of longer-term performance.
Sustainability and integrated reporting
The board of directors through its audit committee should review the reporting of sustainability
issues in the integrated report, ensure that it is reliable and there is no conflict with the financial
information. Adequate information on the company’s financial and sustainability performance
should be provided and there should be commentary provided on the results and plans to
build on the positives and deal with any negatives. External assurance should be obtained for
material sustainability issues. A company is required to produce an integrated report each year
and the emphasis should be on substance over form. Integrated reporting is in line with the
view that strategy, governance and sustainability are inseparable. Companies should ensure
that sustainability is integrated with its normal business operations and sustainability criteria
should be included in performance evaluation. There is the global reporting initiative (GRI),
which offers guidelines on sustainability reporting.
South African companies are regarded as world leaders when it comes to sustainability and
triple bottom line reporting. Yet, South Africa faces daunting environmental challenges not
only from the effects of climate change but also from the impact of its mining legacy. The impact
of gold mining on Gauteng’s water table is expected to have significant environmental impacts.
South Africa faces significant challenges in relation to inequality, unemployment, health care,
educational standards, crime and other social dimensions that require the corporate sector and
government to deal with in order to ensure the sustainability of South Africa’s economic model.
Risk management
Risk management forms a key component of King IV. The board is responsible for the
governance of risk, and is required to report on the effectiveness and process of risk
management as well as the effectiveness of the company’s system of internal controls. Internal
audit is required to report and assess a company’s internal controls and risk management.
Whilst many areas of risk management are beyond the scope of this book, we will focus on
financial risk management in Chapter 18.
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Information Technology (IT) and its role in corporate finance
Why is IT critical for financial management? The efficient functioning of capital markets relies
on IT systems. Financial models and programs play a pivotal role in the design of financial
instruments, risk analysis and valuations. Throughout this text, we will refer to the use of Excel
financial models in applications such as loan amortisations, portfolio construction, option
pricing models, project evaluation and valuations. We will use methods such as data tables,
goal seek, scenario manager and Monte Carlo simulation. Major providers of Enterprise
Resource Planning and Customer Relationship Management systems include Oracle, SAP
and Microsoft.
When we analyse and value companies, we need to consider the ability of the company
to be able to manage IT risks and its ability to use IT to create value. For example, Edcon
is able to manage its inventory and the distribution of 275 million units only due to its IT
capabilities, which is provided by Accenture. At the same time, IT can change suddenly and
make a company’s business model obsolete. When we value companies we need to increasingly
take into account IT risks and capabilities. Furthermore, technology, information and data
analytics form critical components of a company’s strategy. King IV refers to technology and
information in order to highlight the increasing importance of the management of data to firm
sustainability.
Solvency and liquidity tests
The Companies Act, 2008 imposes duties on directors to apply solvency and liquidity tests in
respect to transactions such as, the payment of dividends or distributions to shareholders, share
buy-backs, financial assistance to third parties for the acquisition of the company’s shares, and
loans and financial assistance made to related parties. Essentially, the board is required to be
satisfied that after the transaction, the company’s assets (fairly valued) exceed its liabilities
and that the firm will be able to pay its debts as they come due over the following 12 months.
Otherwise the directors may be personally liable for any loss. In corporate finance, these tests
will normally be applied when the company is considering making dividend distributions or
undertaking share buy-backs or when the company is considering corporate restructuring. We
will evaluate these tests in greater detail in Chapters 16 and 17.
Business rescue
The Companies Act imposes a duty on the board to consider instituting business rescue
proceedings, as outlined in the Companies Act, if the company is financially distressed. We
will examine the workings of the business rescue provisions in Chapter 17.
Does corporate governance pay?
A number of studies1 have found that there are positive effects for companies that focus on
improving their corporate governance structures. The return on assets was 19% better for
well-governed companies and return on equity was 24% better. Companies with effective
corporate governance structures achieve higher valuations. In South Africa, Abdo and Fisher
(Accountancy SA, May 2007) found that companies that achieved a high level of corporate
governance disclosure scores, significantly outperformed companies with low corporate
governance scores. In a study of 169 South African listed firms, Collins Ntim (2013) found
a statistically significant and positive association between good corporate governance and
corporate financial performance (SA Journal of Economics, 81(3), 373–392).
1
See Anson, White & Ho (2003) “The Shareholder Wealth Effects of Calpers’ Focus List”, Journal of Applied
Corporate Finance, 15(3) and Henry (2008) “Corporate Governance Structure and the Valuation of Australian
Firms: Is there Value in Ticking the Boxes”, Journal of Business Finance & Accounting, 35(7).
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A McKinsey survey of large institutional investors found that investors place corporate
governance at the heart of investment decisions. Investors were prepared to pay a premium of
12–14% in North America and Western Europe and a premium of 20–25% in Asia and Latin
America, and a premium of over 30% in parts of Asia and Africa for companies demonstrating
high governance standards. For South Africa, investors were prepared to pay a premium of
22%. Accounting disclosure was a key concern and investors wished to see more independent
boards and the adoption of more effective board practices.
Auditors
Investors and financial managers rely on the integrity of financial statements. In corporate
finance, we use financial statements to value companies and make investment decisions and we
rely on auditors to certify that the financial statements fairly present the financial performance
and position of a company.
Yet corporate scandals such as Enron, WorldCom and Lehman Brothers have shaken the
confidence that investors have in auditors and accountants. Arthur Anderson (Anderson) was
one of the “Big Five” public accounting firms in the world at the time of the Enron collapse.
It had over 80 000 employees, 350 offices in 84 countries and 100 000 clients. Anderson went
down with Enron but was Enron really the cause of Anderson’s demise? Not really. Rather, it
was the loss of its reputational integrity. Anderson earned only about 1% of its revenue from
Enron entities. However, criminal investigation of Anderson and evidence of obstruction of
justice, led to many of Anderson’s other clients racing for the door and appointing other more
reputable audit firms. The association with Anderson was undermining their own reputations.
As clients left en masse, Anderson crumbled very quickly. It was difficult to forget Anderson
staff shredding incriminating documents through the day and night.
In 2010, Ernst and Young were implicated with the downfall of Lehman Brothers as it
permitted the company to shift assets and liabilities off its balance sheet (Statement of
Financial Position). This made Lehman Brothers seem less geared than it really was. This was
called “window dressing”, a term which reflects the ethical ambiguity of accounting. Other
terms such as creative accounting, and earnings management do not sound like serious ethical
dilemmas but really are.
In South Africa, in 2018 we find that Deloitte is under investigation by the Independent
Regulatory Board for Auditors (IRBA) for its audit of African Bank Investments Ltd (ABIL)
which collapsed in 2014. IRBA is also reviewing the Deloitte audit files relating to Steinhoff
which lost over R230 billion in market capitalisation due to accounting irregularities. It was
German regulators and particularly the report of a short seller that led to the discovery of
accounting irregularities at Steinhoff. KPMG and Nkonki face significant reputation loss due
to inappropriate practices and in fact Nkonki has ceased to exist as a firm. KPMG will be a
smaller firm than before due to the loss of clients.
Auditors have not been that effective in uncovering fraud. A major USA study found
that auditors uncover only 11% of frauds. Employees, the media, analysts and short-sellers
are more effective at uncovering fraud. It is true that investors do place value on audited
financial statements and the role of the audit in protecting the integrity of financial statements.
An unqualified audit report does offer reasonable assurance about the integrity of financial
statements. It is important as a first step in any analysis to check that the report of the auditor
states that the financial statements present fairly, in all material respects the financial position
and performance of a company and that the financial statements have been prepared in line
with the Companies Act and International Financial Reporting Standards.
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FROM THE REAL WORLD … APPLICATION OF KING IV BY NETCARE
So, how do companies report on the application of the King IV principles? Netcare is a leading
hospital group in South Africa. In its 2017 King IV application register it states the following
“outcomes” for the application of selected King IV principles
SELECTED KING IV PRINCIPLES
NETCARE OUTCOMES
Principle 1: The governing body should lead
ethically and effectively
• Included in the FTSE/JSE Top 30 Responsible
Investment Index
• Highly rated on the Transparency Index
Principle 5: The Board should ensure that reports
issued by the organisation enable stakeholders
to make an informed assessment of the
organisation’s performance and its short, medium
and long-term prospects.
• Annual integrated report consistently ranked
“excellent” in the EY Excellence in Reporting
Awards
• Assurance on financial information and
certain non-financial performance indicators
has been obtained in line with combined
assurance model
• The Group annual financial statements for
the year were unqualified
Principle 13: The governing body should govern
compliance with applicable laws and adopted,
non-binding rules, codes and standards in a way
that it supports the organisation being ethical and
a good corporate citizen
• No material penalties, sanction or fines for
contraventions of, or non-compliance with,
regulatory obligations during the period
under review
Principle 14: The Board should ensure that the
organisation remunerates fairly, responsibly and
transparently so as to promote achievement of
strategic objectives and positive outcomes in the
short, medium and long term
• 90.06% of shareholders voted in favour of
the remuneration policy at the 2017 AGM
• The Board is satisfied that the remuneration
policy and its implementation reflect
appropriate alignment between the Group’s
strategic imperatives and stakeholder
interests
What does Charlie Munger think about Corporate Governance?
The general premise is that management are willing to make decisions that will enhance their
own interests above the interests of the company. In practice executives are offered incentives
such as performance linked remuneration to ensure the alignment of the interests of the
executives and shareholders. An independent board of directors are appointed in order to
monitor management and set remuneration, there is an internal audit department, there is a
risk management committee and other committees. There are often complex remuneration
contracts. Therefore, there is a network of controls and incentives to try and influence
management behaviour. Charlie Munger (the partner of Warren Buffett) has a different view.
Munger believes in simplicity and fewer rather than more controls. He states that:
A lot of people think that if you just had more process and more compliance – checks and doublechecks and so forth – you create a better result in the world. Well, Berkshire has had practically
no process. We just try and operate in a seamless web of deserved trust and be careful whom we
trust.
If there is trust, one does not have to monitor. Munger goes on to state that; “we want very
good leaders who have a lot of power, and we want to delegate a lot of power to those leaders”.
Munger goes on to state that “truly responsible, reliable systems must be designed so that
people who make the decisions bear the consequences”.
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Munger refers to the Romans who required the builder of any bridge to stand under the arch
once the scaffolding was removed. A CEO that stays around for only a few years may not bear
the consequences of his or her decisions and never gets to stand under the bridge and may
leave when the cracks start to appear. Munger also indicates that it is important to “create
human systems that are hard to cheat”. Munger believes in conservative accounting and states
that ninety-nine percent of the problems come from too optimistic accounting. Aggressive
behaviour leads to aggressive practices but perhaps it is the person that leads the accounting.
Munger believes in modest executive compensation. Directors should also be modestly
paid in order to ensure a greater degree of independence and Munger refers to what a US
cabinet member said that “no man is fit to hold office who isn’t perfectly willing to leave it
anytime”.
The reality is that corporate governance systems have become much more complex and
layered and Munger recommends simplicity and avoidance of excessive controls. The shift by
King IV to focus on principles rather than rules is aligned to this view.
CASE STUDY: TIGER BRANDS AND SOCIETY
Tiger Brands is the leading manufacturer and distributor of branded food products in South
Africa. Its brands include Tastic, Albany, Jungle Oats, Fatti’s and Moni’s, Koo, All Gold, Black
Cat, Oros and Beacon amongst other brands. The group put its costly investment in Dangote
Milling in Nigeria behind it when it announced the disposal of this loss-making unit for R1
on 13 December 2015. The financial performance of Tiger Brands by early 2018 reflected the
following:
■■ A 50% increase in the share price from 22 February 2016 to 20 February 2018, from R300
to R450
■■ A falling debt/equity ratio indicating lower financial risk
■■ A return on invested capital of about 18% that exceeded its cost of capital
■■ A healthy gross margin of 33% and an improving operating margin of 14.5%
■■ An EBITDA in 2017 of over R5 billion.
Yet in March 2018, it was found that the world’s largest listeriosis outbreak, according the
World Health Organisation (WHO), could be traced back to Tiger Brands’ Enterprise factory
in Polokwane, which manufacture polonies and other ready-to-eat meat products. This had
involved an investigation by the National Institute for Communicable Diseases (NICD) over
many months looking for the source of the ST6 strain of the listeria monocytogenes pathogen.
This was a human tragedy as over 193 people lost their lives as reported by the NICD on 13 April
2018 and over a 1000 people were infected. Tragically, 81 deaths related to babies younger than
28 days.
Although, the NICD and Tiger Brands did offer sometimes conflicting reports about
communications and timelines, the reality is that there is something clearly wrong when close to
200 customers die from eating the Enterprise meat products. Either the current food standards
are inadequate or processes are at fault. There may be problems with the supply chain as the
bacteria may relate to imported products.
Tiger Brands recalled its Enterprise products and closed a number of its facilities. The group
was expected to incur material costs relating to the recall and lost sales as well as suffer significant
damages to its reputation. Demand for its Enterprise products and all processed meats will be
affected and there may be irreparable harm to the Enterprise brand. The Tiger Brands CEO
who was appointed in 2016 promised to implement protocols at their facilities that would require
zero evidence of listeria.
The group faces class-action law suits and investigations by the state in regard to any breaches
of food safety standards. Estimates of costs and damages of R1 billion and R1.4 billion were
reported in the media. An article in Business Day (26/4/2018) asked the question, “How can
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Tiger restore trust?” It compared Tiger’s response to RCL Foods (owner of Rainbow Chicken)
which had immediately recalled products and shut down its polony plant.
The impact on Tiger Brands’ share price was dramatic. The share price fell from about
R450 to about R350 in just over 3 weeks. Tiger Brands has 192.07m shares in issue and so this
represented a loss of about R19.2 billion. Although the share price recovered to about R395
by 16 April 2018, this still represented a loss of close to R10 billion. It may well be that this
represents only a temporary setback and perhaps this tragedy will lead to more stringent food
safety standards and/or greater compliance to enhanced standards and testing procedures by all
food producers in South Africa. It may also mean that there is a greater risk to food safety due
to different strains of pathogens. The experience reflects how important the triple context is in
business. Consumers and society are important stakeholders in the Tiger Brands business and
it is critical for the company to manage the relationships with its key stakeholders, particularly
when a crisis unfolds. Can society trust Tiger Brands in the future? It is up to the board of Tiger
Brands to ensure the safety of its products, and enhance the tests for bacteria at its production
facilities to ensure that this does not occur again.
9 CORPORATE STRATEGY
Corporate strategy is about direction and action. It is important that a company sets out
its mission and objectives and understands the business environment that it is operating in.
Financial management decisions should be aligned with a company’s corporate strategy. A key
question relates to how a company should create a sustainable competitive advantage in each
sector it operates in. Should the firm focus on low cost or differentiation strategies? Often a
company needs to decide what businesses the company should be in and then focus on making
decisions that increase the value of the firm. This also means that sometimes a firm should
divest of poor-performing divisions.
In order to increase the value of the firm, we need to understand the competitive landscape,
and future likely developments in a sector. Further, management incentives need to be aligned
with a company’s strategy. Firms will often use models such as Porter’s Five Forces, SWOT
analysis and PESTEL analysis in order to frame their strategic analysis.
Porter’s Five Forces Model
Michael Porter of Harvard, based on extensive research and company interviews, set out the
five forces that impact on corporate and industry profitability. These are:
1. Level of rivalry amongst existing companies in the sector;
2. Existence and threat of substitute products;
3. Threat of new entrants and existence of barriers to entry;
4. Bargaining power of a firm’s customers; and
5. Bargaining power of a firm’s suppliers.
Each force involves understanding the interaction of a number of factors. For example, high
exit costs and spare capacity will mean that firms will tend to compete aggressively with each
other thereby reducing operating margins. Often, firms will analyse investment decisions in
terms of Porter’s Five Forces model. Therefore we will expand in greater detail on Porter’s
Five Forces model, which enables us to place a company’s corporate strategy in context.
Rivalry among existing firms
High industry growth should enable firms to achieve a higher level of profitability, as existing
firms will not need to compete to grow. Slow market growth will lead to a higher level of
rivalry and lower profitability as firms can only grow by taking market share away from their
competitors. If there are a large number of firms in the industry, then this will increase rivalry
leading to lower prices and lower returns. However, it may be seen as positive, as the potential
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to grow market share exists if the company is introducing a product or distribution concept
that adds value and changes the rules of the game.
If a company has high fixed costs relative to variable costs, and the industry is characterised
by high fixed costs, then capacity utilisation is critical and firms will compete aggressively in
order to achieve a higher level of sales and production. Any expansion or new investment by a
company will involve a higher level of risk as the reactions of existing firms will be aggressive
and will reduce the potential returns, at least for a while. However, although the expansion or
new investment may involve high fixed costs, the adoption of new technology may result in a
significant reduction in the marginal production cost per unit. For example, the introduction of
the Airbus A350 will reduce significantly the operating cost per air mile, particularly in relation
to fuel costs and will result in an increased capacity for airlines investing in the A350.
If the product is highly perishable or involves high storage costs, then the potential for
aggressive competition increases as firms may try and offload inventory very quickly. This
will increase risk and reduce profitability. However, investments that add value in relation to
distribution efficiencies will create greater value. For example, the investment in technology
that allows firms to react more quickly to changes in consumer buying trends means that the
risk of any investment is reduced.
If switching costs are high, then initial entry into the market may result in a reduction in
risk if industry growth is high. In a static market, high switching costs will mean that new
products will find it difficult to obtain market share. However, existing companies may be able
to protect margins. Although low switching costs may result in the company being able obtain
market share, it will also mean that competition will remain high and returns will be subject to
competitive pressures. Low levels of product differentiation will also increase competition and
increase the risk of any new project in terms of its longer-term returns, although the absence
of strong brands may allow the firm to penetrate the market.
If there are high exit barriers and excess capacity, then firms will compete aggressively as the
cost of leaving the industry is high. If any investment involves highly specialised equipment,
then the market for equipment will be limited and the value of this equipment will reflect the
state of the industry. The firm will be exposed to high levels of risk as the abandonment option
has a low value. The diversity of participants in an industry and other effects of globalisation
may mean increased competition which will lead to lower margins.
To summarise, rivalry and price competition will be intense and profitability will be
constrained if the following factors apply:
■■ There are many competitors of a similar size
■■ The industry growth rate is low, so that current companies have to compete aggressively
in order to grow market share
■■ There are high exit barriers
■■ Low switching costs apply so that customers can move easily
■■ Companies produce similar products and services
■■ There is spare capacity
■■ The products or services are perishable
Profitability will be enhanced if there are only a small number of competitors, there is a
high industry growth rate, exit barriers are low, there are high switching costs, products are
differentiated, there is no spare capacity and products are not perishable.
Threat of substitute products
The existence of substitute products restricts the ability of firms in an industry to raise prices.
Substitute products come from outside the industry but perform a similar function. In the
beverage sector, the ability to generate supernormal profits from the sale of aluminium cans
is limited due to the existence of glass and plastic bottle containers, which serve the same
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function. TV may become increasingly subject to competition from the Internet as faster
broadband speeds become more widespread. Changes in technology may create substitute
products and whole industries may be subject to change and some products are more at risk
due to changes in technology. Yet the power of brands and image is powerful in differentiating
products such as footwear and clothing. In the food and the over-the-counter pharmaceutical
sectors, the power of brands has lost some value due to the increasing focus by the major
retailers on house (no name) brands. If any investment by a company is subject to the threat of
substitutes then this will increase firm risk and reduce profitability.
Threat of new entrants and barriers to entry
If a firm operates in an industry that has high barriers to entry, then the risk of operating in
the sector will be lower, as higher returns will be sustainable. However, high barriers to entry
will mean a higher level of risk and high start-up costs for companies trying to obtain entry to
a particular industry sector.
High barriers to entry exist where economies of scale require new companies to invest large sums
to achieve a meaningful market presence. For example, entry into the pharmaceutical industry
requires large investments in research and development and the building of relationships in the
health sector chain of medical practices and hospitals. In the soft drinks sector, substantial sums
are required for brand advertising and a few companies may control the distribution channels.
Further, the reduction in unit cost may require material investments in plant and equipment.
Government and legal barriers to entry may exist as companies may be required to adhere to strict
regulatory regimes and product evaluations such as the introduction of new drugs. The airline
industry and utilities are subject to regulations, which may act as barriers to entry.
It does mean that, for firms in the industry, any returns generated from investment decisions
may be sustainable, thereby reducing the risk of individual projects. However, the initial costs
will increase for a company trying to enter an industry, although the effect of government
regulations may serve to improve the competitive position of the firm once it has made a
successful entry. The concentration in the banking sector means that the major banks are now
effectively too large to fail and the government would step in to prevent bank failure due to
the overall impact of any failure on the financial system. This makes it relatively more difficult
for smaller banks to compete and banking regulations are a significant burden for the smaller
banks in relation to the large banks. However, industry concentration in a few large banks in
South Africa, allegedly charging high fees and providing poor service with complex pricing
structures, with a focus on closing branches, and a dependence on legacy systems created the
environment which enabled the entry of Capitec Bank. It was only in 2002 that Capitec Bank
listed at R2 per share (The share price was R300 in 2014). The focus of Capitec is on providing
a simplified service, charging low fees, employing advanced IT systems and credit evaluation
systems, enabling cash withdrawals when shopping at the major retailers, providing banking
services to the lower-middle income market and growing its branch network.
Patents and licences create barriers against competition for a defined time period. If a
company is involved in the production of products with patents, then this will enable the
company to generate higher returns and maintain a sustainable competitive advantage and
charge higher prices. This reduces the risk of the company. However, the patented products
may have high levels of risk due to high research and development costs. There may be
first-mover advantages in terms of setting industry standards, obtaining government licences
and learning economies, which may deter other entrants from entering the sector. Firstmover advantages may reduce the risk of investing in a new project, although this reason
for competitive advantage is balanced by the high risk of failure, in that there may be good
reasons that the promised new market does not exist. For example, the investment in fibre
optic cabling by the telecom companies in the USA overstated the potential demand for
broadband services. Specialised technology, plant and equipment create a barrier to entry,
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as the cost is not reduced by the disposal of assets at reasonable values if the project fails.
The investment in generalised factory space and assets such as trucks is not risky as the
value of these assets is not dependent on the performance of the project and its related
industry sector. Further, existing firms will tend to react very aggressively to new entrants
when specialised equipment is required for any investment, thereby increasing the risk to
companies making the decision to enter the sector.
Establishing distribution channels and relationships will mean high costs and higher risks
attaching to failure. For example, a new food product requires acquiring shelf space but there
are only a few major retail chains. If Pick n Pay, Woolworths, Spar and Shoprite do not agree
to carry the product, then sales will not occur. Competing products may have already built
up relationships with the major chains, which make it more difficult to obtain shelf space.
Is the product a high turnover item and does the firm advertise the product independently?
Acceptance may mean a substantial return and rejection by the major chains will mean absolute
failure. Project risk will therefore increase if we’re not sure that the major chains will allocate
shelf space to the product.
Companies that have effective control over distribution networks will be able to earn
higher returns. For example, Coca Cola controls an extensive distribution network. An
existing motor vehicle manufacturer such as BMW has an extensive network of dealerships.
New auto competitors will find it hard to break into the sector, as it will need to set up a
dealer network in order to compete effectively. Therefore, companies with dealerships or
retailers in the right locations will be able to earn higher returns.
Bargaining power of buyers
If there are many suppliers and only a few buyers, then buyers will tend to determine the price
and terms of the relationship. If a buyer purchases a significant proportion of the company’s
output, then the buyer will set the price. If products are not differentiated and switching costs
are low, then buyers will tend to be more aggressive in setting prices and quality standards.
Another factor is that the product must constitute a large percentage of cost to the buyer
for it to attract the appropriate level of attention. The above point has been made of the
relative position of buyers and suppliers in the food retail sector whereby the four chains have
huge bargaining power in relation to independent suppliers. This is underscored by the ability
of the retail chains to offer house or no-name brands, which reflects an ability to engage in
backward integration. Buyers may be weak if suppliers are able to create their own distribution
network, there are high switching costs and if there are many buyers. It is critical to evaluate
the bargaining power of buyers if the project involves the supply of new products. Yet, an
existing firm with an established industry presence with a portfolio of existing products may
find that the marketing of a new product may be facilitated owing to the national presence
of a retailing chain. This will reduce the risk of introducing a new product and will certainly
expedite the national availability of the product. In another example, there are many component
manufacturers in the automotive industry but there are only a few car manufacturers.
Bargaining power of suppliers
If there are only a few suppliers and many customers, then the power of suppliers will be high.
For example, the power of Intel and Microsoft in relation to the PC manufacturers is high.
In South Africa, Tiger Brands is a major supplier of branded food products, but this power is
counterbalanced by the power of the retail chains. De Beers (now part of Anglo American)
was the major supplier of diamonds worldwide for many years and still sells about two thirds of
world production of gem diamonds. The pharmaceutical companies have held onto significant
levers of power in relation to the pricing of patented drugs. If the company is able to exercise
significant power over its suppliers, then the company will be able to reduce the cost of its
inputs and increase its profit margins.
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Competitive strategies: cost leadership and differentiation
There are two generic competitive strategies that firms may adopt to sustain a competitive
advantage: cost leadership and differentiation. A cost leadership strategy involves the firm
being a low-cost producer and protects the firm against the potential for a price war. Airlines
are investing in new planes such as the Airbus A350 and the Dreamliner in order to reduce
fuel costs and other operating costs per air mile. The investment by South32 (previously BHP
Billiton) in the Mozal aluminium smelter involved an investment of about US$2.2 billion, which
represented a high fixed cost. However, the smelter was able to produce aluminium at the time
at a cash cost of less than US$600 per tonne, which was significantly less than other major firms
in the industry. This reduced the real risk of the investment as the investment resulted in the
company being in a cost leadership position relative to other firms in the industry and in terms
of utilising capacity, as the LME (London Metals Exchange) price was unlikely to fall to such
levels2. Therefore, cost leadership will reduce risk if the result is the firm being able to produce
at a lower cost than other industry participants and if existing firms have already committed to
large capital investments in the sector. To achieve cost leadership, firms will focus on achieving
economies of scale, cost control, reduce investment in inventory, standardise product designs,
incur low R&D and achieve high levels of production and distribution efficiencies.
A differentiation strategy involves the development of unique products and services that
permit the firm to charge premium prices. Differentiation may involve R&D capabilities,
and marketing and product development expertise, a focus on quality, timing of delivery and
warranties that will enable the firm to obtain customer loyalty due to the attributes of the
product and the firm. An established firm, which is renowned for the quality of its products,
will imply a lower level of risk for new products.
Cost leadership will enable the firm to cut prices to deter potential new entrants, and also
enables the firm to offer lower prices to powerful buyers and allows the firm to compete on
price. Differentiation will result in customer loyalty and will result in a fall in the power of
buyers, as there are fewer product alternatives. Further, differentiation reduces the threat of
substitutes and enables the firm to retain customers.
Investments might be viewed as investments impacting on operating effectiveness and this
may reflect lower costs of production or distribution or improvements in quality. The difference
in incremental costs may indicate a positive NPV. Yet in terms of meeting competition, the
relevant issue is of lost sales and revenue if we do not invest in new manufacturing processes.
In the cost-effectiveness scenario, the issue revolves around competitors obtaining cost
advantages, which will affect the firm’s position and its ability to compete in the future. Risk
may rise due to the effects of global competition and the geography of decision-making in a
volatile and complex business environment.
SWOT analysis
A company will often face internal and external forces, which impact positively or negatively
on the company’s performance. SWOT analysis is employed to set out a company’s internal
strengths and weaknesses and a company’s external opportunities and threats. A company
should focus on strategies and decisions that will make the most of its strengths and avoid
decisions that will bring to the fore its weaknesses. For example, a major strength for a
pharmaceutical company may relate to its strong portfolio of drugs under patent. A further
strength may relate to its wide distribution network and sales and marketing teams. A major
The global aluminium sector has been going through a difficult time in recent years due to overproduction and
falling prices. Although the cost of production at South32’s Mozal and Hillside smelters remains lower than its
major competitors which are closing smelters due to losses, the low cost of production at the Mozal and Hillside
smelters is due to the low cost of electricity supplied in terms of long-term contracts. The low cost of production
has allowed the company to ride out these stormy times so far. The recovery in the aluminium price in 2017 and
2018 has improved the prospects for the smelters.
2
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weakness may relate to the fact that the company has few new drugs under development,
particularly in the biotech sector. To address this weakness, the pharmaceutical company may
adopt a strategy of increasing its research and development capabilities. It may also decide to
purchase or enter into a joint venture with a smaller biotech company, which has a number of
new drugs in the “pipeline” but has weak distribution and marketing capabilities.
Opportunities and threats relate to external factors. A threat may relate to the entrance
of a new competitor. For example, the entrance of Wal-Mart into the South African market
may pose a threat to a company such as Pick n Pay. A stronger Rand exchange rate would
be expected to increase the margins of a company such as Mr. Price that imports most of its
clothing products from Asia. A weak Rand may be a threat for a company such as Mr. Price.
Table 1.4 sets out a possible template for a SWOT analysis.
Table 1.4 SWOT analysis framework
What are some examples of strengths, weaknesses, opportunities and threats?
Strengths: Strong brands, IT capabilities and systems, product quality, distribution channels,
human resources, state of the art equipment, management team, customer loyalty programmes,
low debt, accreditations, prices, certifications, supply chain management.
Weaknesses: Lack of skills, weak brands in certain segments, problems with customer retention,
unreliable suppliers, lack of new product development, problems with product quality, lack of
training, weak supply chain, over-dependence on CEO, lack of IT capabilities, poor financial
position and lack of capital to finance expansion.
Opportunities: New technologies, falling interest rates, changing demographics, changes
in consumer tastes, an increasing Black middle class, opening of African markets,
improved logistics and improvements in distribution channels, reduction in tariffs, access
to overseas markets, access to credit by potential customers, vulnerable competitors,
vertical integration.
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Threats: Changes in technology may make products obsolete, changes in consumer tastes,
rising interest rates, changes in the exchange rate, inflation, tariff and tax increases, changes in
government regulations, climate change, seasonality, loss of key staff.
Let’s evaluate some examples. MTN and Shoprite have expanded into Africa and have been
successful in the execution of this strategy. This represented a strategic opportunity for these
companies. Yet, challenges remain in relation to political risks, government regulations and
problems with local partners. Companies that did not succeed include Tiger Brands, PPC and
Woolworths.
The private health care providers in South Africa face daunting challenges in terms of changes
in government regulations. There are skills shortages due to nurses going overseas. Yet a rising
Black middle class is expected to significantly benefit the private health care companies as
well as the pharmaceutical companies such as Aspen, as more people obtain access to private
health care and join medical aids.
What are the potential problems with using SWOT analysis? It is subjective. Therefore, it is
important to prioritise and indicate what factors will have the most material impact on the
company’s operations, assets and levels of profitability. Do a what-if analysis – what is the
impact on the company’s profitability if the Rand appreciates by 10%. SWOT analysis can be
simply a laundry list. This may be dangerous. Just because we have set out all the factors, does
not mean that we have dealt with all the issues.
We need to set strategies in place. A weakness or threat should be matched with a strategy
to deal with the threat or weakness. Sometimes this is not possible, but we should endeavour
to adopt strategies as far as possible to deal with weaknesses and threats. We have no control
over exchange rates but we may create flexibility to change suppliers quickly, if required. It is
useful to be specific. If we have a cost advantage in relation to the cost of production, then
indicate what this is. Perhaps we can produce at R600 per ton whilst our competitors can only
produce at R900 per ton. Further we should set out strategies to leverage our strengths and
take advantage of opportunities.
PESTEL analysis
PESTEL analysis refers to a framework for considering the Political, Economic, Social,
Technological, Environmental and Legal factors that will have a material impact on a
company’s operations and level of profitability. What do these factors include?
Political: taxation, tariffs, labour legislation, environmental regulations, trade barriers, impact
of government policies such as income grants, provision of housing, health care regulations,
education and infrastructure. Companies may win or lose if there are changes in these factors.
A company providing low cost housing will gain from a focus by government to provide low
cost housing to South Africa’s population.
Economic: interest rates, economic growth rate, inflation rate, exchange rates. Lower interest
rates may mean a greater level of disposable income and greater spending by consumers
thereby increasing the demand for a company’s products.
Social: population growth rates, changing demographics and age distribution, focus on safety,
rising Black middle class, changing values, use of credit, focus on food quality and health,
increase in demand for travel. A growing population and a growing Black middle class have
increased the demand for the products of many South African companies. Companies such as
Truworths have benefited greatly by a rising Black middle class with access to credit.
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Technological: advances in software and IT capabilities, research and development, automation,
robots, rate of change in processes. The improvement in IT has enabled companies to monitor
sales very carefully so that inventory management and orders reflect product sales particularly
for companies such as Edcon, Truworths and Shoprite. Inventory control due to scanning has
enabled a lower investment in inventory and lower losses from shrinkage and obsolescence.
Environment: Climate change and the impact of South Africa’s mining legacy will impact on
the agricultural sector and other sectors that make material use of water resources.
Legal: Increasingly, legal risks relating to competition law, environmental law, consumer
protection laws, access to credit laws, employment and labour laws, health and safety
regulations are all having a material impact on corporate strategies.
Sustainability related issues
The JSE introduced its Socially Responsible Investment (SRI) Index in 2004. All companies
that form part of the JSE All Share Index are evaluated in terms of environmental, social,
governance and related sustainability concerns and climate change impacts. This was known
as triple bottom line reporting. In early 2018, there were 76 constituents of the index. The SRI
Index criteria are aligned with international benchmarks. Environmental evaluation is based on
a company’s impact in terms of climate change, air pollution, water pollution, waste and water
consumption. In relation to society, a company is expected to treat all stakeholders fairly and
with dignity, develop and empower its employees, ensure the attainment of key labour standards
and employee relations and promote safety at work as well as the health of its employees.
In 2015, the JSE adopted the FTSE Russell ESG ratings process to introduce a FTSE/JSE
Responsible Investment Top 30 Index (market-cap weighted) and an equally weighted FTSE/
JSE Responsible Investment Top 30 Index which comprises the top 30 companies ranked on
the basis of FTSE Russell ESG ratings. The leading companies included in the latter index are
Netcare, Grindrod, MMI Holdings, Gold Fields, Compagnie Financiere Richemont AG, BHP
Billiton, Truworths, BAT and Barloworld.
Internationally, the Global Reporting Initiative (GRI) is an organisation that sets guidelines
on sustainability reporting. The GRI guidelines include, economic, environmental, and social
categories. The social category has sub-categories, which include labour practices and decent
work, human rights, society and product responsibility. The GRI sets out the aspects of these
categories and the following are just a few aspects per category.
The Equator principles apply to banks lending mostly in developing economies. Banks that
adopt the equator principles make a commitment to fund projects only if these projects
adhere to sound environmental and social standards. Projects are evaluated in terms of their
social and environmental impacts – there are international benchmarks used in relation to
labour working conditions, emissions, community impacts, and health and safety concerns.
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10 BEHAVIOURAL FINANCE
Behavioural finance is about how psychology affects financial decision making. It is based on
the premise that investors and financial managers are not always rational and that financial
markets are not always efficient. There may be limits to arbitrage and prices do not always
reflect all available information. We are human and subject to errors of judgement and biases
and we place too much faith on rules of thumb (heuristics) and short cuts which may lead
to sub-optimal financial decision making. It is important to avoid or address biases such as
overconfidence, self-attribution, conservatism, confirmation, anchoring and loss aversion to
ensure optimal financial decision making. In Appendix 1.1, we explain behavioural finance
in greater detail and set out the most common biases and heuristics with examples. In later
chapters, we will not only explain how to undertake the analysis of investment and financing
options, we will also include possible biases that may impede effective financial decision
making.
11 STRUCTURE OF THE TEXT
We use a framework which gives an overview of financial management as a whole. The text is
divided into five sections, each building on knowledge gained from the previous section.
This first section has placed financial management as a discipline into perspective and has
focused on the role of the financial manager within the economic environment.
The second section will deal with the essential concepts and tools necessary to perform
the task of a financial manager. It is essential, for example, to be in a position to analyse
annual financial statements, to understand concepts relating to the time value of money and
the interaction of risk and return, and to be familiar with the principles of valuation and the
cost of capital. Once these principles have been mastered, progress can be made toward
understanding the variables interacting in the financial management decisions.
The third section focuses on the investment decision. We have identified two different
types of investment decision, namely the decision to invest in long-term operating assets
(capital budgeting), and the decision to invest in short-term operating assets (working capital
management).
The fourth section explores the financing alternatives. The balance between equity and
debt within the capital structure is considered as well as the effect of this balance on the cost
of finance. The possibility of leasing as a finance option and the implications of using foreign
finance become important issues in this section. Whilst the dividend policy of a company could
be discussed under a separate section, we have considered it to be a part of the financing
decision and have thus kept this issue together with other financing questions.
The fifth section has identified a number of integrated but specific topics. These include
mergers and acquisitions, risk management, international financial management, business
planning and financial modelling and finally we will come full circle by exploring corporate
strategy and business models in greater depth than we have done in this chapter.
SUMMARY
The financial management function focuses primarily on decision-making with regard to
investment and financing decisions of a business enterprise. The primary objective of the
financial manager is to maximise the value of the firm. This objective is attained through the
analysis and selection of investment opportunities and the use of alternative sources of funds.
Further, adherence to good corporate governance as set out by King IV and a focus on
ethical leadership, the environment and creating a positive impact on society will ensure that
the company has a sustainable future. Financial decision-making should take place within the
context of a company’s strategy.
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APPENDIX 1.1 AN INTRODUCTION TO BEHAVIOURAL FINANCE
Traditional finance theory assumes that investors and financial managers are rational and that
markets are efficient. What if investors are not always rational?3 What if markets are not always
efficient? If markets are efficient, then share prices reflect all available information and it is
difficult to earn above average returns without taking above average risks. New information is
quickly impounded into the share price and risk-free opportunities are quickly arbitraged away.
Behavioural Finance postulates that markets are not always efficient and investors are not
always rational. Behavioural finance is about how psychology affects financial decision making.
We as humans are imperfect and subject to emotions and errors of judgement. Biases impact
on human judgement in relation investment and financing decisions and there may be limits to
arbitrage.
In this book, we are going to explain how you should go about making financial decisions in
terms of traditional finance but we also want you to be aware of how biases can impact on financial
decision making in the real world. For example, in project evaluation we will explain how firms
should use net present value (NPV) to make a project investment decision by discounting future
cash flows and comparing this to cost. However, perhaps a financial manager is overly confident
in his or her abilities to forecast future cash flows. Perhaps a financial manager is subject to overoptimism or has based future cash flows of the project on only the performance of the sector in
recent years. In an alternative scenario, perhaps a financial manager is subject to the sunk cost
fallacy and is planning to continue with a project only because the firm has already invested, say
R100m, in the project. Effectively, the manager is throwing good money after bad.
Whilst it is not necessary that all investors are rational, financial theory assumes that rational
investors and rational managers dominate (in relation to the weight of funds under management)
so that markets are rational and prices fully reflect all information – or at least reflect all public
information.
Yet, we do not wish to overstate irrationality either. Yes, it is true that we are subject to
errors of judgement and biases but we need to place this in context. The expression that fools
and their money are soon parted is prescient to our view that markets can be unforgiving in
the longer term to irrational investors and managers. Perhaps it is possible to take advantage
or guard against biases in the short term whilst financial managers should not allow biases to
influence long-term investment or financing decisions.
In this book we will often step back and ask the question; what does Warren Buffett think?
Buffett’s value investing methodology is based on his mentor, Benjamin Graham, who stated that
in the short term the market is a voting machine but in the long term it is a weighing machine.
Eventually, share prices should converge to true value.
In alignment with market efficiency, we see that fund managers do not consistently outperform
the market index after fees and in recent years we have seen significant inflows into unit trust
funds, exchange traded funds (ETFs) and mutual funds that simply track the market indices such
as the S&P500 and the JSE ALSI. Yet, it is also true that the average fund has returned about 10%
per year in the USA and the average investor in those funds has only made about 6% per year –
perhaps due to fees, trading costs and selling early and buying late through investment cycles.
Coming back to the premise about irrational investors, we also know that we are unlikely
to meet investors that are trying to lose as much money as possible and take on as much risk as
possible. That would be truly irrational. Whilst we are imperfect, we are not mad, except perhaps
in times of market bubbles (bitcoin?). What is more likely is that we let greed and fear overly
influence our decision making in sub-optimal ways. Investors and financial managers are prone
to biases, emotions and taking short-cuts which may lead to incorrect decisions.
This is understandable in relation to the growing complexity of processes, the volume of
available information, our limited cognitive resources and the limits on our time to make
decisions due to onerous deadlines.
The absence of rationality may be due to memory limitations,
information, time constraints and human nature.
3
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What are the limits to arbitrage that may influence prices?
Informed investors should take advantage of mispricing. Yet mispricing may not permit true
arbitrage. For example, assume a South African listed company owns a 33% stake in a listed
entity in China which is worth $175bn and yet the company’s own market capitalisation is only
$121bn. This means that the company’s other numerous investments are worth a negative $54bn.
Surely, this reflects mispricing and investors should sell in China and buy in South Africa. Does
this happen in practice? Yes, the above situation reflected Naspers and its investment in Tencent
in China in March 2018. Let’s assume that this situation represents mispricing for now. Investors
may borrow Tencent shares for 3 months and sell these shares today and use the proceeds to buy
shares in Naspers. But perhaps this current irrational situation actually gets worse over the next 3
months and the valuation discount widens as the Naspers share price falls and the Tencent price
rises. In three months’ time the investor has to sell Naspers at a discount and buy back Tencent
shares at a premium – essentially losing money by buying high and selling low4. John Maynard
Keynes wrote that the market can stay irrational for longer than you can stay solvent. There may
be factors such as transaction costs, limits on short sales as it is difficult to borrow shares, capital
controls, dilution due to future share issues, information gathering costs and so on to explain the
limits to arbitrage. The risk of short sales can be high.
Biases and heuristics (short-cuts/rules of thumb)
Heuristics or mental shortcuts enable us to make quick decisions and judgements and are helpful
when they assist us to make quick sense of a complex environment. We often make decisions
without really thinking and short-cuts and rules of thumb are fast, efficient and can often be
correct. However, heuristics can also lead to systemic errors and cognitive biases which means
there is a tendency to draw incorrect conclusions in given circumstances. For example, we make
decisions based on what quickly comes to mind and often this may be correct but in the context
of investments, we may not factor in business cycles or volatility in long-term returns if we only
focus on recent share market performance. How we describe or frame information influences
decisions. Frame dependence indicates that investors will make decisions based on the way that
information is presented. Cognitive biases can also result from social cognition, which reflects us
trying to feel better about ourselves. Self-deception about our abilities means we will be able to
more readily convince others that our abilities are truly superior. We are also human and subject
to emotions that are often more powerful than reason.
So, what are some of the biases, short-cuts and errors of judgement that we should be aware
of to ensure as far as possible that we make optimal financial decisions? The following are some
biases and heuristics that have been recognised from psychology and behavioural finance studies.
Overconfidence
People are prone to overestimate their own abilities and this includes the ability to forecast
future outcomes and overstate their investing prowess. When combined with over-optimism,
this can lead investors and managers to overstate returns and underestimate risk. This may
be applicable to mergers and acquisitions. Overconfident managers can overestimate returns,
minimise risks and pay too much. Tiger Brands, Famous Brands, PPC and Woolworths are
successful companies in South Africa and yet incurred significant financial losses by acquiring
companies in Nigeria, the UK, Kenya and Australia. Perhaps overconfidence played a role in
such investments. We will come back to these companies in Chapter 17. Checklists, quantitative
processes, diversification, appointing a devil’s advocate in the firm, welcoming alternative views
and extensive due diligence may help in checking overconfidence and over-optimism.
Quite serendipitously, Business Day ran an editorial about two months later on 11 May 2018, titled “Dangers
loom in Naspers tale: The first problem is the discount between Naspers’s market capitalisation and the value
of its stake in Tencent is widening dangerously”.
4
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Self-attribution bias
This relates to the comforting trait of attributing success to skill and failure to bad luck, or more
likely to changes in the economic environment. It is rare to read an integrated annual report
and find the CEO blaming himself/herself or his/her executives for the poor performance of the
firm. Invariably, blame is due to economic circumstances, government policies, customers being
under financial pressure, higher interest rates or currency effects. Self-attribution may lead to
delusional albeit comforting thoughts but it is not useful for learning, and improving future
financial decision-making.
Conservatism
Managers and investors often stay loyal to prior beliefs despite the arrival of new information.
Managers may be slow to adjust prices, valuations, costs and projections from an initial value.
Analysts who forecast future earnings for a company are often slow to adjust projections from
their initial forecasts even though a company reports higher earnings for a number of subsequent
periods. Conversely, a financial manager may hold onto higher forecast sales projections even
though sales figures have fallen over a number of periods. Once formed, an opinion may be
cast in iron and often a company will appoint a new CEO to ensure that the company changes
direction. When BHP was required to adjust from an expansionary phase to a new phase which
required cutting back on projects, the company appointed a new CEO.
Anchoring
Individuals use an initial value which they adjust to arrive at an estimated value. An initial value,
even when not relevant, may influence and result in a biased estimate. Cost or the share price is
an important anchor in determining value and may influence financial decision making. Often,
we may find it difficult to make an objective decision because we are too “anchored” on an initial
estimate, or value or price.
Loss aversion, prospect theory and the disposition effect
In finance theory, investors focus on expected return and risk. Investors are assumed to measure
risk on the basis of volatility and variability of possible returns. Higher volatility should result in
a higher return. Prospect theory indicates that investors are much more sensitive to losses than
gains. It is estimated for example that if you are offered an investment with a 50% chance of a
R10 000 loss, then to get someone to accept this, you would need to offer a 50% chance of a gain
of about R25 000. An investor feels the pain of losses more keenly than the joy of gains.
The disposition effect refers to the propensity of investors to sell winners and hold onto losers.
Assume an investor has purchased Share A at R100 and Share B at R100. If Share A appreciates
to R130, and Share B falls to R70, then the investor is likely to sell Share A and hold onto Share
B. This relates to loss aversion as investors wish to avoid losses, and holding onto Share B means
that there is always a possibility that the share price will recover. The evidence in respect to the
wisdom of this strategy is not good. In fact, there is an alternative strategy of “cutting your losses
early and letting your winners run”.
Confirmation bias
This reflects our desire to search for and favour information that supports our pre-existing
views whilst conveniently ignoring or underweighting information that conflicts with our current
beliefs. For example, a company invested significant amounts in the development of a promising
new drug despite indications that side effects may be an issue, but the latter was downplayed
until the evidence was so overwhelming that the drug was finally recalled. Significant costs could
have been saved by acting earlier. In another example, a CEO of an iron-ore mining company
decided to expand production as he was of the view that the iron-ore price would continue to
appreciate as it had been doing in recent years. The price thereafter started falling but this
was viewed as simply a blip, and the CEO focused on favourable reports about future demand
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for iron-ore and steel and ignored or downplayed other reports that indicated falling demand.
Confirmation bias reflects wishful thinking which has a long historical arc.
Francis Bacon in 1620 in Novum Organum wrote:
The human understanding when it has once adopted an opinion … draws all things else to support
and agree with it. And though there be a greater number and weight of instances to be found on the
other side, yet these it either neglects or despises, or else by some distinction sets aside or rejects.
In 421BC, Thucydides wrote that:
… it is a habit of mankind to entrust to careless hope what they long for, and to use sovereign reason
to thrust aside what they do not fancy.
Francis Bacon also wrote that “man always believes more readily that which he prefers”.
Availability and representativeness
Financial managers and investors overstate the probabilities of recent experience and recent
observations in making decisions. We give undue weight to recent events in framing our view
of the future. We assume that the recent past will continue. For example, if commodity prices
have been rising over the last few years, then investors will tend to assume that prices will
continue rising even though commodity prices are cyclical. Looking back 10 years may have
offered investors a different viewpoint about the future. The recent past is fresh in our memory
which may then lead to biased forecasts of future prices. Representativeness is where investors
evaluate an investment based on superficial attributes rather than by undertaking a complete
and objective analysis. Representativeness can represent a useful short-cut (heuristic) in the face
of information overload but may lead to fundamentally wrong decisions. For example, investors
often assume that good companies are good investments. A company like Clicks has excellent
management and great results but it may not be a great investment at the current price. At the
same time, a badly managed company can be a good investment due to a very low price.
The availability rule of thumb means that decision makers assess the likelihood of an event
based on the ease that occurrences are brought to mind. This may refer to recent trends in
earnings, prices or specific events. We would expect that more common events will be fresh in our
minds and so this can be a useful heuristic, but not always. Warren Buffett invested in American
Express when it was going through a difficult period due to losses arising from the salad oil
scandal. Although the company’s share price fell significantly and it was being hammered in the
financial media, Buffett could see that this was only a temporary setback. About 20 years ago,
Shoprite experienced inventory losses due to theft, resulting in a 46% fall in net profit. This and
adverse media reports led to a fall in the share price but this was just a temporary and shortterm setback. Nothing in the underlying business had changed and it was highly probable that
Shoprite would adopt systems to ensure that this would not happen again. Bloomberg reported
that a small company, Long Island Iced Tea Corp. changed its name in December 2017 to Long
Blockchain Corp. and promptly saw its share price rise by about 200%5. This is an example of
representativeness, although there are less kind words to explain this phenomenon.
Inertia
Procrastination and inertia are powerful forces and a firm may delay the investment in new
technology even though the firm recognises the need to change its processes and business model.
The outcome is uncertain and so the company decides to stay with what it knows even though this
may have long-term negative consequences. Inertia may relate to regret avoidance which leads
management to taking a wait and see approach. Sometimes this can work out and may prevent
companies making expensive mistakes but at other times, if you wait you can get run over. The
5
Thanks to Jean-Sebastian Correia for bringing this to my attention.
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opposite of inertia is not reckless decision-making. It means detailed and objective analysis. A
company can make a small investment in new technology or processes and still retain its current
business. It then has the option to upscale quickly once there is greater certainty about how the
industry is going to develop and evolve.
Herding behaviour
This is a powerful heuristic or rule of thumb. Herding refers to being influenced by peers to follow
trends or to follow the crowd when it comes to investing. For example, assume that Company X has
developed a new software application and there is positive news regarding take-up of this software
by clients. As more investors invest in Company X, and the share price increases, this further
attracts more investors. This is perhaps because it is a good investment, perhaps it is because
investors fear missing out or perhaps investors are there for the ride and hope to get out prior to
any decline. Herding behaviour can lead to the correct valuation of a company but it may also lead
to asset bubbles, which is what happened with the internet boom and recently with cryptocurrencies
such as bitcoin. Often, personal conviction is overturned by the power of crowds. During the
internet bubble, Buffett’s company, Berkshire Hathaway’s share price fell significantly as he was
supposedly out of touch for not following the crowd. As he said, one should be greedy when others
are fearful and be fearful when others are greedy. An upward trend in price or earnings may mean
that there is real reason for the optimism but it could also reflect “irrational exuberance” or fraud
and misrepresentation. Value investors such as Allan Gray and Warren Buffett often search for
companies that are out of favour and they are also referred to as contrarian investors. At the same
time many unit trust fund managers are said to follow investing strategies that follow the market
and are referred to as closet index huggers. In relation to South African financial managers, there
has been herding behaviour regarding expansion into Africa. The pioneers such as Shoprite and
MTN were followed later by other companies who determined that expansion across Africa was of
strategic importance and valued by their shareholders. The rush to join the momentum of investing
in Africa may have led to a lack of due diligence and overpaying for investments. The same was
true in regard to the wave of European and US companies investing in emerging markets from
2010. Playing catch-up involves danger. Shakespeare wrote that one should go “wisely and slow:
they stumble that run fast” and van Goethe wrote that one should proceed “without haste, but
without rest”. More sage advice from the value investor Howard Marks is that “what the wise man
does in the beginning, the fool does in the end”.
Hindsight bias
This is where past outcomes seem obvious and predictable and we tell ourselves after the fact
that we knew all along how things would unfold. Once we know the outcome and reasons for an
event, we tend to overstate our abilities to have predicted that such an outcome would occur.
This may then lead us to be overconfident about future decision-making.
Ambiguity aversion and familiarity bias
People do not like ambiguity and are highly cautious about what they do not know. A familiarity
bias means that investors are likely to invest only in large companies listed on the JSE and this
may lead to a failure to diversify adequately. Whilst there may be good reasons for investing in
what you know, it is important to consider the costs of inadequate diversification and the loss of
opportunities due to this bias. In the corporate sector, companies may not be willing to invest
in new technologies and may remain with outdated methods because “this is the way it’s always
been done”. Advances in disruptive technologies means that staying with what you know may not
be enough and may lead to corporate failure or at least the destruction of margins. At the same
time, it is also true that when venturing abroad or investing in new technologies, we should apply
a greater degree of analysis and due diligence.
The endowment effect, money illusion and mental accounting
The endowment effect indicates that the value of an asset increases with ownership. There is
a connection, a commitment simply because we own the asset. In financial decision-making
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this means that we may hold onto assets longer than we should. Money illusion reflects the
tendency of individuals to value money in nominal terms rather than in its purchasing power
or in real terms. A future promise in nominal terms will be valued more highly than merited
by its future purchasing power. An insurance broker, financial planner or asset manager would
prefer to promise you R5m in 20 years’ time, if you invest R1m today without indicating that
the purchasing power of R5m in 20 years’ time may only be worth R1.85m today. You may wish
to believe this as well. In relation to gains, individuals are risk averse and in relation to losses,
individuals are risk seeking. In terms of mental accounting, we keep funds in separate accounts
for different purposes and varying risks. We may keep funds in different buckets and we allocate
funds to low-risk investments and other funds to high-risk projects. Investors may more readily
spend dividend income than capital gains which requires the sale of shares.
Conclusion
These are only a few of the biases that may affect financial decision making. As we go through
some key chapters in the book, we will come back to these biases and evaluate their possible
role in portfolio management, risk management, valuations, cost of capital, capital budgeting,
and financing decisions. We will also refer to rational financial managers making decisions in a
world of irrational investors. On a lighter note, whilst we are going to address the need to remove
biases from decision making, perhaps biases (beliefs?) define who we are. Francis Bacon in his
essay on Truth states:
Doth any man doubt, that if there were taken out of men’s minds, vain opinions, flattering hopes,
false valuations, imaginations as one would, and the like, but it would leave the minds of a number
of men, poor shrunken things, full of melancholy and indisposition, and unpleasing to themselves.
A symphony of biases may lead to discord in relation to financial decision making. For example,
overconfidence is in harmony with the confirmation bias, as we value information which aligns
with our prior beliefs. We remain loyal to our initial estimates and only adjust slowly to new
information in terms of the conservatism bias and our tendency to anchor on a particular value.
Even if decisions go wrong, the self-attribution bias will kick in which enables us to apportion
blame away from ourselves so that we never really learn from our mistakes. There are also biases
that are in conflict with each other such as overconfidence and inertia. Whilst we are going to
take you through the theory and practice of financial management (and it may get technical), we
need to also understand that we are human and it is important to be conscious of our biases and
to avoid their effects as far as possible in financial decision making. Warren Buffett states that
“what you need is the temperament to control the urges that get other people into trouble in
investing”. The ancient Greek maxim inscribed at Delphi is also of relevance here: Know thyself.
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APPENDIX 1.2: PROFESSIONAL ETHICS AND CODES OF CONDUCT
The professional accounting associations offer guidance to members facing ethical dilemmas. As
professionals, accountants have an obligation to themselves, their colleagues and their organisation
to adhere to high standards of ethical conduct. In recognition of this obligation, the South African
Institute of Chartered Accountants (SAICA) and other professional accounting bodies have issued
ethical standards in a code of conduct for their members. SAICA has determined that skills and
integrity are the pre-eminent professional attributes of Chartered Accountants in South Africa. The
Code of Professional Conduct of SAICA is consistent in all material respects with the Code of Ethics
for Professional Accountants issued by the International Federation of Accountants (IFAC) and
conforms to the code issued by the International Ethics Standards Board for Accountants (IESBA).
The fundamental principles of the South African Institute of Chartered Accountants Code of
Professional Conduct are as follows6:
A professional accountant is required to comply with the following fundamental principles:
Integrity
A professional accountant should be straightforward and honest in all professional and business
relationships. Integrity implies fair dealing and truthfulness. A chartered accountant will not be
associated with reports, statements or information, which contains false or misleading statements,
or contains information furnished recklessly or omits or obscures information, if such omission
or obscurity would be misleading.
Objectivity
A professional accountant should not allow bias, conflict of interest or undue influence of others
to override professional or business judgements.
Professional Competence and Due Care
A professional accountant has a continuing duty to maintain professional knowledge and
skill at the level required to ensure that clients receive competent professional service. A
professional accountant should act diligently and in accordance with applicable technical
and professional standards when providing professional services. A chartered accountant
shall not perform a professional service if a circumstance or relationship biases or unduly
influences the chartered accountant’s professional judgement with respect to that service. A
chartered accountant should take reasonable steps to ensure that everyone working under
his/her authority has the appropriate training and supervision. If relevant, a chartered
accountant should make clients, employers or other users of the chartered accountant’s
professional services aware of the limitations inherent in the services and should not
undertake any engagement if the chartered accountant is not competent to perform unless
advice and assistance is obtained to carry out the engagement.
Confidentiality
A professional accountant should respect the confidentiality of information acquired as a result
of professional and business relationships and should not disclose any such information outside
the firm without proper and specific authority unless there is a legal or professional right or
duty to disclose. Confidential information acquired as a result of professional and business
relationships should not be used for the personal advantage of the professional accountant
or third parties. A chartered accountant shall maintain confidentiality in social environments
and should be alert to the possibility of inadvertent disclosure to business associates and family
members. Confidentiality of information should be maintained within the firm and extends to
6
The summary is adapted from the Code of Professional Conduct, SAICA. Copyright SAICA. Reproduced
with the permission of SAICA. The rules of ethical conduct of the CIMA and ACCA are similar to those of
SAICA.
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information disclosed by prospective clients. The principle of confidentiality continues even after
the end of relationships with a client.
Chartered accountants may disclose confidential information if authorised by the client, if the
chartered accountant is required to respond to an inquiry by a regulatory body, or if disclosure
is required by law.
Professional Behaviour
A professional accountant should comply with relevant laws and regulations and should avoid
any action that discredits the profession.
Each of these principles is discussed in greater detail in the Code and readers should visit the
SAICA website, www.saica.co.za for the complete Code of Professional Conduct.
The Chartered Financial Analyst (CFA) Institute has issued a Code of Ethics and Standards of
Professional Conduct7 to guide the actions of investment professionals. The CFA Institute states
that adherence to ethical standards is fundamental to ensuring that the public maintains its trust
in global financial markets.
The CFA Institute’s Code of Ethics requires its members to:
■■
■■
■■
■■
■■
■■
Act with integrity, competence, diligence, respect, and in an ethical manner with the
public, clients, prospective clients, employers, employees, colleagues in the investment
profession, and other participants in the global capital markets.
Place the integrity of the investment profession and the interests of clients above their
own personal interests.
Use reasonable care and exercise independent professional judgement when conducting
investment analysis, making investment recommendations, taking investment actions, and
engaging in other professional activities.
Practice and encourage others to practice in a professional and ethical manner that will
reflect credit on themselves and the profession.
Promote the integrity and viability of the global capital markets for the ultimate benefit of
society.
Maintain and improve their professional competence and strive to maintain and improve
the competence of other investment professionals.
The CFA Institute’s Standards of Professional Conduct covers seven broad areas;
professionalism, integrity of capital markets, duties to clients, duties to employers, investment
analysis, recommendations and actions, conflicts of interest and responsibilities as a CFA
Institute member or candidate.
Professionalism
Members are required to understand and comply with all relevant laws and regulations. Members
are required to be independent and maintain objectivity and should not make misrepresentations
in regard to investment analysis or other professional activities. Further, members should not be
dishonest, engage in fraud or any other activity that impacts negatively on their professional
reputation, competence or integrity.
This section draws from the Standards of Practice Handbook, 11th edition (2014), which is published by
the CFA Institute. Copyright 2014, CFA Institute. Reproduced with permission from CFA Institute. All rights
reserved.
7
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Integrity of markets
Members must not act on material non-public information that could affect the value of an
investment, nor engage in practices that could distort prices or impact on trading volumes in
order to mislead other market participants.
Duties to clients
Members need to be loyal to their clients, exercise reasonable care and apply prudent judgement.
Members should place the interests of their clients above their own interests and above the
interest of their employer and deal fairly and objectively when providing investment analysis,
providing recommendations or undertaking other professional activities. Any investment
recommendation should be the result of inquiry of suitability in relation to a client’s financial
situation, investment objectives and portfolio. The reporting of investment performance should
be accurate, fair and complete. Members should keep client information confidential, unless the
member is required by law to disclose such information.
Duties to employers
Members are required to act for the benefit of their employer and should not disclose confidential
information. Members should avoid receiving gifts or compensation that may create conflicts
with the interest of their employer. Members should try and ensure that anyone subject to their
supervision complies with applicable laws, rules, regulations and the Code and Standards.
Investment analysis, recommendations and actions
Members are required to be diligent, independent and thorough in analysing investments, and
making recommendations, which are supported by research and analysis. Members should
disclose to clients the principles and processes employed to analyse investments, select securities
and construct portfolios and employ judgement in identifying the important factors to their
analyses and to communicate these to their clients. Members are required to disclose any
significant limitations and risks associated with the investment process. Members must retain
appropriate records.
Conflicts of Interest
Members are required to disclose all matters that could impair their independence and
objectivity. Investment transactions for clients should take priority over any transaction for the
benefit of a member. Referral fees should be disclosed.
Responsibilities as a CFA Institute member
Members should not undertake any action that compromises the reputation or integrity of the
CFA Institute or the CFA designation.
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APPENDIX 1.3: STAKEHOLDER CONSIDERATIONS AND GOOD CORPORATE
CITIZENSHIP
By Johnathan Dillon M.Com CA(SA)
Johnathan is currently a corporate consultant. Prior to this he was Associate
Professor and Division Head of Management Accounting and Finance within
the School of Accounting at NMMU. He has a Masters in Finance and is a
Chartered Accountant. He achieved a top 10 position in the 2005 SAICA
Qualifying Examination Part I. He has been actively involved in SAICA’s
ITC examination processes. Research interests include capital budgeting,
valuations and leasing.
Who are a company’s stakeholders? What classifies a company as a good corporate citizen?
Many people incorrectly think that a company’s shareholders are the only stakeholders or
the only stakeholder group which a company should consider when doing business based
on its primary objective of creating value. Furthermore, often there is an incorrect notion
that companies which donate large sums of money to charitable causes are good corporate
citizens. This section aims to dispel these misconceptions through summarising some of the
key concepts surrounding corporate citizenship and stakeholder theory.
Corporate citizenship is defined by the Corporate Citizen Research Unit at Deakin
University in Australia as:1
“a recognition that a business, corporation or business-like organisation, has social, cultural and
environmental responsibilities to the community in which it seeks a licence to operate, as well as
economic and financial ones to its shareholders or immediate stakeholders. Corporate citizenship
involves an organisation coming to terms with the need for, often, radical internal and external
changes, in order to better meet its responsibilities to all of its stakeholders (direct or indirect), in
order to establish, and maintain, sustainable success for the organisation, and, as a result of that
success, to achieve long term sustainable success for the community at large.”
The above definition emphasises a number of important issues, with the main theme being
the requirement for the management team of a company to not focus solely on the company
and its shareholders’ needs. A company should rather consider all stakeholders when doing
business in order to ensure the long-term sustainability of its business as well as the community
and environment within which it operates. This encompasses the concept of corporate
social responsibility which requires a company to take responsibility for its impact on the
environment and social welfare. A good corporate citizen is therefore essentially a company
which considers all stakeholders and accepts that it has a responsibility to its local community
and the natural environment. The community and environment within which a good corporate
citizen operates would therefore be considered by the good corporate citizen when making
any substantive business decisions but still with the aim of delivering satisfactory returns for
shareholders.
In this regard, annually the Corporate Responsibility (CR) Magazine publishes a list
of America’s 100 best corporate citizens on their website (http://www.thecro.com and click
on RECOGNITION) based on companies’ environmental, climate change, human rights,
employee relations, corporate governance, philanthropy and financial rankings. In 2018,
Microsoft was placed top of the list with other well-known companies in the top 10 including
Accenture plc (2), Intel Corp. (4), Cisco (7), Johnson & Johnson (9) and Nvidia (10).
Interestingly, the CR Magazine awards “yellow cards” and “red cards” and on their 2017
list Microsoft received a “yellow card” caution as two former employees were implicated in a
corruption case involving bribes to Romanian officials in relation to the purchase of software
licences. In 2017, Johnson & Johnson received a red card as multiple lawsuits were filed
against the company relating to claims that talcum powder causes ovarian cancer and Johnson
& Johnson knew and did not disclose this to the public. If a company is awarded a “red card”
then it is removed from the list.
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Identifying and managing stakeholders (stakeholder analysis)
From the aforementioned discussion it is evident that when a company operates then,
in addition to the local community and natural environment, all stakeholders (not only
shareholders) need to be considered. A stakeholder of a company is regarded as any entity,
natural or juristic, which has an interest in the company and either impacts or is impacted by
the company’s operations. The major stakeholders of most companies are indicated in Figure
1.11.
Figure 1.11 Stakeholders of a company
Stakeholders commonly fall into one of three categories, namely internal stakeholders,
connected stakeholders and external stakeholders. Furthermore, each stakeholder has
particular interests and can exert influence in a particular way over the company in which it has
an interest. Table 1.5 indicates the three categories together with examples of the particular
interests of the various stakeholders and how they can exert influence over a company.
One of the challenges for a company is to balance the often conflicting interests of its
various stakeholders. For example, shareholders want an appropriate return on their
investment (based on the risk to which they are exposed) which may be possible through
mechanising the company’s production process (reduction in labour costs, quicker production
time, less wastage, safer operations etc.). However, mechanisation leads to job losses which
conflicts with the need for job creation of employees, government, trade unions and the
local community. This example is currently a major challenge for the South African mining
industry. The world’s top three platinum producing companies located in South Africa, Anglo
American Platinum, Impala Platinum and Lonmin, made their intention to mechanise blasting
and rock drilling processes clear in the media in 2014. This came after three years of labour
turmoil, which climaxed with a five month long wage strike during 2014, as well as pressure by
government to make mine shafts safer following reported fatalities. This will not be an easy
decision for these mining companies to implement as there is guaranteed to be resistance from
workers and their trade unions.
Other conflicting relationships have been covered in Chapter 1, namely the conventional
agency problem between shareholders and management as well as the agency problem that
can arise between shareholders and the providers of debt finance (lenders).
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Stakeholder theory was initially covered in a book written by R. Edward Freeman, entitled
Strategic Management: A Stakeholder Approach (1984). Subsequently stakeholder theory has
evolved but essentially there are two alternative views to stakeholder theory. The weak view is
one where stakeholders are seen as necessary and good in light of the fact that they are needed
for a company to fulfil its primary objective of maximising the wealth of shareholders. When
this view is taken, stakeholder relationships are appreciated and the company “partners”
with stakeholders to create value for shareholders. The strong view goes further where each
stakeholder is seen as having an independent right to being considered and looked after
outside of the role that it plays in creating shareholder value. With the strong view a company
recognises that stakeholders have this independent right as the company is afforded the
privilege of operating by society and its various stakeholders. Therefore with the strong view
a company aims to balance the demands of all its stakeholders, one of which is value creation
for shareholders. Considering the fact that management are a stakeholder, this could lead to
them favouring their interests over those of other stakeholders when following the strong view
(amplifying the conventional agency problem). Furthermore, if management are accountable
to all stakeholders then there is a sense that they are in fact accountable to no one. The weak
view of stakeholder theory is therefore favoured whereby stakeholders are to be considered
but the primary objective of the company remains shareholder value maximisation.3
Table 1.5 Stakeholder categories, interests and influences
Category
Stakeholder
Interests
Influence
Internal
Management (including
directors)
Remuneration, job
security, status, job
satisfaction
Decision maker (possible
agency problem),
resignation
Employees
Remuneration, job
security, job satisfaction,
safety
Level of work performance
(quality), industrial action,
resignation
Shareholders
Return on capital invested,
risk exposure
Director appointments, sell
shares
Providers of debt finance
Interest and capital
repayment
Withdraw debt facility,
enforce loan covenants,
force liquidation
Customers
Quality, value for money,
service
Reputation, legal claims,
repeat business or move
to a competitor
Suppliers
Payment, profitability,
future business
Non-supply, inferior service
or quality, high prices,
withdraw credit facility
Advisers
Payment, future business,
adding value
Withhold advice, inferior
service
Competitors
Industry reputation,
industry associations, new
developments
Rivalry, strategic alliances,
takeover
Government (local and
national, including tax
authorities)
Legal operations, tax
collection, job creation
Laws and regulations,
taxes
Industry associations and
trade unions
Members’ rights
Lobby government, legal
action, industrial action
Local community, public at
large, interest groups
Environmental protection,
job creation, social
responsibility
Publicity, demonstrations,
lobby government
Connected
Connected
(cont.)
External
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Stakeholder relationships need to be managed and this largely depends on the level of interest
of the stakeholder in the company’s operations and the degree of influence (power) the
stakeholder can exert over the company (as indicated in Table 1.5). In this regard the powerinterest matrix illustrated in Figure 1.12 is useful. This matrix was originally developed by
Aubrey Mendelow and subsequently adapted and simplified by Gerry Johnson and Kevan
Scholes.4
Figure 1.12 Mendelow’s power-interest matrix
Plotting stakeholders on the power-interest matrix assists a company in determining how
significant its various stakeholders are and how it should deal with particular stakeholders. For
example, a customer may fall into quadrant A based on the fact that it comprises a small portion
of the company’s sales (low bargaining power) and the item purchased may be a commodity
in which case it can be obtained elsewhere (low level of interest). In such a case the company
should expend minimal effort on managing its relationship with the customer; however, where
a customer has more power and a higher level of interest, the relationship needs to be more
closely managed. Shareholders normally fall into quadrant D, while government usually falls
into quadrant C which a company should merely aim to keep satisfied. The local community
within which a company operates is normally placed in quadrant B as it is very interested in the
company’s operations but the community’s power is limited, although protests can influence
other more powerful stakeholders.
Stakeholder relationships should continually be managed and an analysis of stakeholders
should be performed whenever a company makes project investment and other strategic
decisions. A particular decision should be evaluated in terms of its impact on all stakeholders,
bearing in mind each stakeholder’s degree of power and level of interest as indicated by
Mendelow’s matrix. Essentially the company needs to determine whether a strategic decision
under consideration is acceptable to their stakeholders. This links with criteria often used to
evaluate potential strategic options, namely suitability, acceptability and feasibility as outlined
below:
■■ Is the strategy suitable? Does it fit in with the company’s vision and mission?
■■ Is the strategy acceptable? Is it acceptable to stakeholders based on expected profitability,
risk, environmental impact etc.?
■■ Is the strategy feasible? Does the company have the necessary resources?
When managing stakeholder relationships it is also important for a company to measure
the satisfaction of its various stakeholders. This will give the company an indication as to
whether it is successfully managing its relationships with its stakeholders. Although measuring
stakeholder satisfaction is often difficult due to the subjectivity thereof and it often being
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qualitative in nature (e.g. where questionnaires are used), the following are examples of how
satisfaction can be measured:
■■ Shareholders – trading of shares (buying or selling), movement in share price
■■ Employees and management – staff turnover rates, remuneration policies relative to the
market
■■ Customers – percentage on-time delivery, price relative to competitors
■■ Local community – nature and extent of publicity
In conclusion, this section clearly highlights the importance of stakeholders and the need for
a company to consider and balance the interests of all its stakeholders. In doing so a company
will not only be a good corporate citizen but it will also ensure the long-term sustainability of
its operations.
References:
1.
2.
3.
4.
Work and Family Researchers Network, 2014. Corporate Citizenship, Definition(s) of | Work and
Family Researchers Network. [online] Available at: http://workfamily.sas.upenn.edu/glossary/c/
corporate-citizenship-definitions [Accessed 15 November 2014]
CR Magazine, 3BL Media Corporate Responsibility Magazine’s 100 Best Corporate Citizens 2018.
[online] Available at:http://www.3blassociation.com/files/exV4MF/CR_Summer%2018_100%20
Best_revised.pdf [accessed 31 October 2018]
Nordberg, D., 2011. Corporate Governance: Principles and Issues. London: Sage Publications, pp.
42-43.
Olander, S. & Landin, A., 2005. Evaluation of stakeholder influence in the implementation of
construction projects. International Journal of Project Management, 23, p. 322.
Q
QUESTIONS
Question 1.1
Identify the fundamental objective of the financial manager.
Question 1.2
How do you expect deregulation to affect industry sectors and investment decisions? For example,
what happens if government permits deregulation in the electricity sector and permits the entry
of suppliers other than Eskom? Telkom have lost their monopoly. What effect has this had on
Telkom’s returns and investment decisions?
Question 1.3
Why do companies need a financial manager? What does a financial manager do?
Question 1.4
To what extent may the goals of the firm differ from those of the financial manager?
Question 1.5
Outline the most significant economic developments which the financial manager will need to
consider in making investment and financing decisions.
Question 1.6
Distinguish between operating assets and financial assets. Under what circumstances may one be
preferable to the other?
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Question 1.7
Distinguish between capital markets and money markets. Under what circumstances do financial
managers seek finance from these two markets respectively?
Question 1.8
What are the advantages of the company form of business organisation?
Question 1.9
Outline four criteria which will result in differing financial impacts as a result of the choice of
business organisation.
Question 1.10
Mr Knight has obtained a patent on a new device that lures insects and electrocutes them once
they touch a grid inside the device. He is at the stage of manufacturing the first units and marketing
the device and has asked you to advise him whether he should operate as a sole trader, within a
partnership, a private company or public company. How would your advice change as the entity
grows over time?
Question 1.11
Distinguish between profit maximisation and value maximisation. Are these two concepts linked or
mutually exclusive?
Question 1.12
Assume that you have been appointed as the financial manager of a large listed company operating
a chain of supermarkets throughout South Africa. Identify some specific investment decisions and
some specific financing decisions which you may be called upon to make.
Question 1.13
A business that is expanding is considering using debt to fund the planned projects. They plan
to arrange the financing first and then consider the expansionary projects once they know what
money is available. Comment on whether the financing decision should be considered before the
investment decision.
Question 1.14
From your understanding of financial accounting, what are your thoughts about the accuracy and
value of financial statements, such as the Statement of Comprehensive Income and the Statement
of Financial Position, for use by financial managers.
Question 1.15
Explain economic value added (EVA) and indicate why a company may have a positive accounting
profit and a negative EVA.
Question 1.16
Indicate why maximising accounting profits is not a useful corporate finance objective.
Question 1.17
Indicate why agency problems exist between management and shareholders. What factors will
ensure an alignment between the objectives of shareholders and management?
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Question 1.18
Energy Ltd’s management, who have been issued with a substantial number of share options, are
considering investing in a high risk project which offers potentially significant returns. News of this
proposed project has been leaked into the market, and the ordinary share price immediately rose
but the price of the company’s corporate bonds fell sharply. Explain why this may happen.
Question 1.19
Why are the concepts of risk and time value of money important in making investment and financing
decisions?
Question 1.20
In the context of control, risk, transferability and tax rates, discuss the advantages of being a sole
trader, in a partnership or a company.
Question 1.21
Two multinational companies have recently published their objectives:
Company A:
“Our company’s objective is to focus on the maximisation of global shareholder wealth. We will use
sophisticated measures to maximise cash flow in each country in which we operate. We will also
extensively outsource internationally in order to increase profitability.”
Company B:
“Our company’s primary objectives are to enhance our customers’ satisfaction and to grow our
business. We aim to supply our customers with the highest quality products and provide outstanding
levels of sales and delivery service, incapable of being matched by our competitors, and thereby
increasing our market share.”
Required:
Discuss and contrast these objectives. Comment upon any possible ethical implications of the
objectives.
(ACCA)
Question 1.22
Provide examples of ethical issues that might affect capital investment decisions, and discuss the
importance of such issues for strategic financial management.
(ACCA)
Question 1.23
You are required to analyse the 2018 Integrated Reports of Aspen, and Clicks. Evaluate the
corporate strategies of each firm in terms of Porter’s Five Forces model as is possible from the
information set out in each Integrated Report. [Note – you can download the respective Integrated
Reports from their corporate websites]
Question 1.24
Explain the concept of loss aversion and prospect theory and how this may affect corporate financial
decision making.
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THE TIME VALUE OF MONEY
2-1
THE TIME VALUE OF MONEY
2
IS COMPOUND INTEREST THE MOST POWERFUL FORCE IN THE UNIVERSE?
How do you grow an investment of $1 into $23 367 over 53 years? Yet, this is what Warren Buffett
managed to achieve for his shareholders. Nearer to home, Allan Gray managed to do even better
by growing R10 into R226 793 over 44 years for Allan Gray’s investors. What is the compound
return that Warren Buffett and Allan Gray achieved for their shareholders and how do their returns
compare to investing in the market index? We will answer this question and analyse the formulae and
application of time value of money principles to real world problems. We will also analyse the role of
interest rates and determine how to value bonds.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Understand the role of time value of money in finance and understand the concept of
compound interest.
■■ Use formulae, tables, financial calculators and spreadsheets to determine:
–– the future value of a single amount invested today;
–– the future value of an annuity;
–– the present value of a single future amount;
–– the present value of an annuity;
–– the present value of a perpetuity;
–– the present value of a growing perpetuity;
–– the present value of a cash flow growing at a constant rate over a period of time;
–– the present value of uneven cash flow streams.
■■ Define and calculate an annual effective rate.
■■ Distinguish between nominal and real interest rates.
■■ Apply compounding and discounting to complex cash flow streams.
■■ Apply time value of money principles to real world problems such as retirement
planning and the valuation of bonds and
■■ Establish the factors that determine the term structure of interest rates.
INTRODUCTION
In this chapter we will learn how to value estimated future cash flows and apply time value of
money principles to such applications as determining the repayments on a loan. The principles
outlined here are fundamental to all aspects of financial management and serve as essential tools
in the activities of the financial manager.
Companies and individuals often have opportunities to earn returns on investments. When
you invest in a savings account, you will earn a return, the interest rate, for a specified period.
When companies invest in plant and machinery, the company is expecting to earn cash flows over
a number of years. When you take out a student loan, you wish to know what the repayments
will be. A financial manager is required to value projects with cash flows that will occur at
different points in time. The timing of cash flows is an important component of corporate finance
decisions. Why is a rand today worth more than a rand in a year’s time? The simple answer is that
you can invest the rand today to accumulate to a larger sum in a year’s time. We are required to
determine future values and present values of cash flows. To do this, we will develop formulae
which we can apply to real world applications.
We can also use Tables which are found at the back of the book. However, increas­ingly we
use financial calculators and Excel or other spreadsheet programs to solve time value of money
problems. Whilst we do not often need the formulae to determine present values and future
values, and we could focus only on the use of financial calculators, it is useful to understand the
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formulae, as these are fundamental to many applications. Further, in the real world, we often
may need to set up our own financial spreadsheet models and we may be required to use the
formulae rather than use functions.
1 FUTURE VALUE
Investors expect to receive a return on their investments in the form of interest or other returns.
We need to increase the original amount invested by adding the interest that accrued during the
time of the investment. Future value is the value in rands that an investment or series of investments
will grow to over a stated time period at a specified interest rate. The following notation will form the
basis of the formulae to be applied in this chapter:
FV:
PV:
r:
PMT:
n:
The amount of cash which will have accrued by a given date resulting from
earlier single sum or periodic investments.
The value of an investment at the beginning of a period, sometimes referred to as
the principal sum.
The interest rate.
The periodic investments or instalments made, excluding single lump-sum
investments. This may occur at the end or beginning of each period.
The number of periods for which the investment is to receive interest.
Single amount, single period
Where a single amount is invested for a period of one year, the calculations are relatively
straightforward.
Example 2.1: Future value: one year hence
An amount of R100 is invested for one year at a rate of 12% p.a. What is the future value of this
investment at the end of the year?
FV = PV (1 + r) (Formula 2.1)
= R100 (1.12) = R112
The interest on the investment is clearly R12, and the future value of the investment after one
year is R112.
Single amount, multiple periods, annual interest compounded
An investment of a single amount accrues interest in each period and, frequently, the interest
is added to the original investment rather than being paid out. This is referred to as compound
interest. This very important concept in financial management results in interest being earned
on interest. The compounding effect has an immense impact on the value of an investment,
especially if the period of investment is lengthy. For example, R100 invested at 15% for three
years, with interest compounded annually, amounts to R152, while if it was left for 30 years, it
would accumulate to R6 621 and if left for 50 years would accumulate to R108 366. If interest
was not compounded in this way, the interest every year would remain at R15 and the investment
would grow by this amount each year and amount to R550 after 30 years or R850 after 50 years.
Interest is not earned on interest. This is referred to as simple interest.
Example 2.2: Calculating the future value: more than one year
An amount of R100 is invested for 10 years at a rate of 12% p.a. compound interest. What is the
future value of this investment at the end of 10 years?
Using Formula 2.1 we know that the future value at the end of year one is R112. If this whole
amount remains invested for another year, the future value at the end of year two will be:
FV = R112 (1.12) = R125.44
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2-3
The interest for the second year is:
R125.44 – R112.00 = R13.44
The interest for the second year is R1.44 higher than for the first year. This is because
interest at the rate of 12% has been earned on the interest of R12 earned at the end of the
first year as well as on the original R100. This can be checked by calculating the interest for
one year on R12 at 12% p.a.
= R12 3 0.12 3 1
= R1.44
In order to develop a formula for compound interest, the following logic can be applied:
For year one
FV = R100 (1.12) = R112
For year two
FV = R112 (1.12) = R125.44
For year three FV = R125.44 (1.12) = R140.50
For year two the calculation could be expressed as:
FV = R100(1.12)(1.12)
For year three the calculation could be expressed as:
FV = R100(1.12)(1.12)(1.12)
This can be generalised to:
FV = PV (1 + r)n(Formula 2.2)
For the example above this is:
FV =
=
=
R100 (1.12)10
R100 3 3.1058
R310.58
It is quite easy to calculate (1.12)10. We can also use financial calculators, Excel spreadsheets
or Table A. Table A, which is given at the back of this text, is referred to as the future
value of R1 table. It is drafted for all the commonly used interest rates for up to 50 different
periods. By consulting Table A and looking for the 12% column and the 10-period row,
the figure 3.1058 will be located. This is multiplied by the principal sum of R100 in order to
arrive at the future value of R310.58.
If only the interest component is required, the principal sum can be deducted. In this
case the compound interest earned for the 10 years is R310.58 less R100, that is R210.58.
We now have a formula for determining the future value and, we can calculate any
missing variable. The effect of compounding on the value of an investment can be remarkable.
The following graph depicts the future value of an investment at an interest rate of 12%,
assuming both compound interest and simple interest. The difference is due to interest
being earned on interest.
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FINANCIAL MANAGEMENT
Figure 2.1 Future values – compound interest and simple interest
Assume that you have always wanted to be a millionaire. Well, if you invest R10 000 today
at an interest rate of 10% for 50 years, you will reach your target of making over a million
rand. Of course, a million rand will mean less in 50 years’ time than it does today.
FV = R10 000 (1 + 0.10)50 = R1.174m
The level of interest rates or returns also has a significant effect on the future value. The
graph below indicates the effect that compounding at different interest rates has on future
value.
Figure 2.2 Future value of single investment of R10 000 at varying interest rates
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2-5
Warren Buffett is one of the world’s wealthiest men and the world’s most famous investor,
worth over $85.3 billion (about R1 045 billion) in 2018. Investing in his company, Berkshire
Hathaway from the beginning of 1965 to the end of 2017 would have resulted in a com‑
pound return of 20.9% per year. Assume that an old uncle invested $1 000 on your behalf in
Berkshire Hathaway at the time. What would you have been worth at the end of 2017? Remember
we are talking about a $1 000 investment 53 years ago. We can use Formula 2.2 as follows:
FV = 1 000 (1+0.209)53 = $23 366 515
Imagine the growth in wealth from $1 000 to about $23.4 million. You could retire before
starting to work. Perhaps, this is why Albert Einstein stated that the most powerful force in
the universe is compound interest. However, assume that your uncle had rather invested the
$1 000 in the general share market (S&P500). This would have resulted in a compound return
of 9.9% per year. What is the accumulated sum at the end of 2017? Applying Formula 2.2 again:
FV = 1 000 (1+0.099)53 = $148 894
What a difference 11% (0.209 – 0.099) per year makes! Over a long period, even a few
percentage points difference add up to a significant amount due to the impact of compound
interest. Of course this is in the USA and we would like to know if you could have done as
well in South Africa. We will come back to this question a little later in the chapter.
Example 2.3: Calculating the principal amount
An investor wishes to invest a sum of money which will accumulate to R310.58 in 10 years’
time. How much must be invested today, if the investor can earn a rate of 12% per year?
Changing the subject of Formula 2.2, it can be stated as:
PV =
=
=
FV
(1 + r)n
(Formula 2.3)
310.58
(1.12)10
310.58
3.1058
= R100
As expected from the results of Example 2.2, the required investment is R100. Table A may
also be used to expedite the calculation of (1.12)10. Looking at Table A, the future value
factor is 3.1058. We can also use a financial calculator. We solve the same problem later in
the chapter using a financial calculator – see Section 4.
Example 2.4: Calculating the number of periods
An investor is informed that an investment of R100 will grow to R310.58. If it is known that
the applied rate is 12%, how many periods are necessary for the R100 to become R310.58?
Developing a formula to solve this would require the use of logarithms. However, by
referring to Table A, and finding the relevant factor, the number of periods can be determined
by inspection as follows:
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FINANCIAL MANAGEMENT
FV ​ or n = [(LN FV – LN PV)/LN (1 + r)]
(1 + r) n = ​ 
PV
310.58
(1.12) n = ​ 
​
100
(Formula 2.4)
= 3.1058
The number 3.1058 is the factor defined in Table A. Because it is known that the interest
rate is 12%, it is possible to move down the 12% column until the number nearest to 3.1058
is found. In this example it is found in the 10-period row. Let’s go back to the formula:
(1.12)n = 3.1058
We can use natural logarithms to solve for n:
nLN1.12 = LN3.1058
n = LN3.1058/LN1.12
n = 1.1333/0.11333
n = 10 years
Example 2.5: Calculating the interest rate
An investor is given the opportunity of investing R100 today with a promised future value of
R310.58 in 10 years’ time. At what rate is the investment accruing interest?
From Formula 2.4, it is possible to make r the subject of the formula as follows:
FV ​(Formula 2.5)
(1 + r)n = ​ 
PV
r = (FV/PV)(1/n) – 1
= (310.58/100)(1/10) – 1
= 0.12 or 12%
Instead of using the formula, Table A can again be used. This time one would search for a
number close to 3.1058 by looking along the 10-period row. Once the closest number to 3.1058 is
located, the column in which it is situated is the required interest rate. We can also use a financial
calculator or Excel spreadsheets to determine the interest rate (See Section 4 on financial
calculators and Excel).
We analysed the performance of investing with Buffett in the USA. What about investing
in South Africa? Allan Gray is one of South Africa’s largest asset management companies.
Allan Gray stated in 2018 that if you had invested R10 000 in June 1974 with Allan Gray
then this investment would have grown to an incredible R226.793 million by 30 June 2018.
If you had invested in the JSE All Share Index over the same period, your R10 000 would
have grown to R9.536 million. Whilst the JSE appears to have offered a very good return,
Allan Gray’s performance seems to have been exceptional. What is the annual compound
return that Allan Gray earned over the period? What is the annual compound return from
investing in the JSE over the same period?
We can work with Formula 2.5 and we will count this as 44 years.
Allan Gray: R10 000 (1+r)44 = R226 793 305
r = (226 793 305/10 000)(1/44) 21 = 25.601% per year
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2-7
JSE All Share Index: R10 000 (1+r)44 = R9 536 015
r = (9 536 015/10 000)(1/44) 21 = 16.873% per year
In fact, Allan Gray has outperformed the JSE All Share Index by 8.728% per year and we
can see what a big difference this can have on the final accumulated amount. Allan Gray’s
investment performance compares well to Warren Buffett’s performance although we need
to be careful as relative performance depends on the beginning and ending period.
Single amount, multiple periods, non-annual compounding
It often happens that an investment offers a rate of interest per annum, but stipulates that
interest will be compounded at different intervals – quarterly or monthly, for example. This
means that interest is added more frequently than once a year. As a result there is more
opportunity for earning interest on interest. The net effect is that a higher return is obtained
on the investment than would have been the case had interest only been compounded
annually. In such a case the quoted per annum rate is called the quoted rate while the true
return in annual terms is higher if the number of compounding periods is more than once a
year, and is called the annual effective rate (see Formula 2.7).
Example 2.6: Future value, interest compounded monthly
An investor deposits R100 into an account which offers 12% p.a. interest compounded
monthly. Find the value of the investment at the end of one year.
Because interest is compounded monthly, it can be said that 12% over 12 months – i.e.
1% interest – is added every month. Using Formula 2.2 it can be seen that the investment at
the end of the second month would be:
FV = R100 (1.01) (1.01)
At the end of the twelfth month it would be:
FV = R100 (1.01)12
= R100 3 1.1268
= R112.68
The extra 68 cents, although not significant over a short period, will compound over longer
periods and can make a considerable difference. The effective rate in this example is
12.68%.
The formula required to generalise this calculation is as follows:
r mn(Formula 2.6)
FV = PV (​​ 1 + ​ 
m ​  )​​ ​
where m is the number of times within a year that interest is compounded and n is the
number of years.
If the investment were made for 10 years, the future value would be:
(
)
× 10
0.12 ​  12
FV = R100 ​​ 1 + ​ 
​​
​
12
120
= R100 3 1.01
= R100 3 3.300
= R330
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FINANCIAL MANAGEMENT
It is clear that Table A can still be used. The difference is that the necessary adjustment
must be made to the rate and the periods in order to read the table correctly. The formulae
and the tables work in periods rather than years. Monthly interest in this case is 1% for 120
periods. Unfortunately, few tables extend as far as 120 periods. Rather use the formula or
a financial calculator.
Annual effective rate
It is useful to be able to convert a quoted or nominal interest rate into an effective interest
rate for many reasons, particularly in order to compare investment alternatives with different
compounding periods. We can accept that two interest rates are equivalent if they have the
same effect, that is, if a single amount invested at one rate and compounded annually for
a length of time accumulates to the same future value as another rate compounded more
frequently.
The effective annual rate of interest is the annual rate that if compounded once a year
would give us the same result as the interest per period compounded a number of times per
year. The effective annual rate is calculated as follows:
rn m
1 + re = ​​ 1 + ​ 
m ​  ​​ ​
(
)
where re is the effective rate and rn the nominal rate, compounded m times annually. This
converts to:
rn m
re = ​​ 1 + ​ 
– 1(Formula 2.7)
m ​  ​​ ​
(
)
Example 2.7: Converting nominal to effective interest rate
Ozbank offers the Ozplan Premium account, an investment account which requires a
minimum investment of R10 000. The account offers an interest rate of 6% per year, interest
compounded monthly. What is the annual effective interest rate?
Using Formula 2.7:
(
)
0.06 ​  12
Effective rate = ​​ 1 + ​ 
​​ ​– 1
12
12
= 1.005 – 1
= 1.06168 – 1
= 6.1678%
This means that 6% per year, with interest compounded monthly is equivalent to 6.168%
per year, with interest compounded annually.
Table 2.1 Effective rates
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2-9
We can use effective rates to compare investments or loans which have the same quoted rate
but different compounding periods. In terms of “truth in lending” rules, banks may disclose
the average percentage yield (APY) which is similar to computing the effective rate. Investec
in May 2018 was advertising a 12-month fixed deposit rate of 7.53% nominal and Investec
indicated that this represented an annual effective rate of 7.80%. The deposit earns interest
on a monthly basis, so there are 12 compounding periods in a year. Is the advertised effective
rate correct? If we apply Formula 2.7, we can see that the effective rate is correctly stated at
7.80% [(1+0.0753/12)12 – 1].
Continuous compounding
So far, in considering an investment which earns interest, we have used annual, semi-annual,
quarterly, monthly or daily compounding. However, why stop there? We could invest so that
interest is earned on interest every hour or every second. What happens is that we approach
a limit. We can see from Table 2.1 that the incremental increases in the effective interest
rate gets smaller as we move from annual to daily compounding. If we extend Table 2.1, then
hourly compounding would represent adding interest of 0.000006849 [6%/(365 3 24)] of the
principal every hour. This would result in an effective rate of 6.18363%. As we approach
infinity in terms of the number of compounding periods, the effective interest rate is
er – 1, whereby e is equal to 2.71828. In our example, if the investment is offering continuous
compounding, then this would result in an annual effective interest rate of:
Annual Effective Rate = 2.718280.06 – 1 = 6.18365%
The future value of an investment earning interest at 6% per year, with interest compounded
continuously, is determined by multiplying the present value by ern. If we were investing
R10 000 at 6% for 10 years, with interest compounded continuously, then the future value
would be:
Future Value = Present Value × 2.71828(0.06 × 10)
FV = R10 000 × 1.822119 = R18 221.19
Alternatively, using the effective annual interest rate:
FV = R10 000 × 1.061836510 = R18 221.19
Apart from simply determining the future value of an investment, continuous compounding
(and discounting) has other uses in finance, such as in the pricing of options.
Interpolation
When using Table A to determine the rate or number of periods, the exact table reading,
referred to as the accumulation factor, is seldom found. In order to obtain more accurate
solutions, interpolation should be used. Although not strictly arithmetically accurate,
interpolation does provide a better answer than estimation.
Example 2.8: Finding the interest rate
An investor deposits R100 into an account which promises a future value of R154 in six
years’ time. At what rate is interest being compounded annually?
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Using Formula 2.4:
FV ​
(1 + r)n = ​ 
PV
154  ​ = 1.540
= ​ 
100
As we know it is for 6 years, by reading across Table A under six periods, we see that a factor
of 1.54 lies between 7% and 8% for 6 years:
Note that the future value of 1.540 lies between 7% and 8%. The difference in the table
readings between 7% and 8% is 0.0862 (1.5869 – 1.5007).
The factor of 1.54 required is 0.0393 (1.54 – 1.5007) above 7%. In order to determine
how far past 7% it is using interpolation, the following calculation is used:
0.0393
3 1% = 0.456%
0.0862
The interest rate so calculated is 7.456% (7% + 0.456%)
Although interpolation may be useful, it is no longer necessary in a world of financial
calculators and Excel spreadsheets [Financial calculator result: 7.4616%].
Series of investments, ordinary annuity (FVA) – multiple investments and multiple
periods
So far we have dealt with a single investment at the beginning of a period and considered
all the variables that can be determined. Investment opportunities are also available that
require a series of payments of a fixed amount for a specific number of periods. These are
known as annuities. For reasons which relate more to consistency of formulation and generally
accepted usage than to practical investment procedure, we will assume that the first instalment
is generally invested at the end of the period. This is known as an ordinary annuity and we
will apply this concept throughout this text unless otherwise stated. We will now develop the
necessary formulae and tables.
Example 2.9: Calculating the future value of an ordinary annuity
An investor pays equal instalments of R100 at the end of each year into a savings account
yielding an interest rate of 12% per year, compounded annually. What is the future value of
the investment at the end of three years?
An ordinary annuity means that the payment occurs at the end of each period and the
following table depicts the cash flows and the investment of each annuity payment.
Table 2.2 Future value of an ordinary annuity (FVA) at 12%
Year end
0
1
2
3
InstalmentR100R100R100.00
(1.12)1
(1.12)
2
R112.00
R125.44
Future value =R337.44
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2-11
The first instalment earns interest for two years, the second instalment earns interest for
one year, and the third instalment receives no interest as it is deposited at the end of Year 3.
This can be expressed as:
FVA = R100 3 1.122 + R100 3 1.121 + R100 3 1.120
= 337.44
If the instalment is taken as the common factor, the future value interest factor of an annuity
can be written as:
3
∑
FVIFA = ​ ​(​ 1.12)​3 – t
t=1
Where t is the period for each instalment, this translates into the following formula:
n
∑
FVIFA = ​ ​​(1 + r)​n – t
t=1
This formula is cumbersome and requires a separate calculation for each of the years. A
more workable formula has been developed which achieves the same result. It is particularly
useful for calculations requiring fractions of rates or periods not provided for in the tables.
[
]
(1 + r)n – 1
FVA = PMT × ​ ​ 
​  ​(Formula 2.8)
r
3
(1 + 0.12) – 1
= R100 × ​ 
​
​  ​
0.12
[
]
= R100 × 3.3744
= R337.44
We can also use Table B to determine the future value of an ordinary annuity. This table is
known as the future value of an annuity of R1 per period and contains the future value interest
factor of an annuity (FVIFA). Table B is closely related to Table A. In fact, Table B is the
accumulation of Table A for n – 1 periods plus a factor of one. This relationship exists as
Table B assumes the payment takes place at the end of the period, while Table A assumes
the payment occurs at the beginning.
n Table A – 1%
Table B – 1%
11.01001.0000
21.0201
e.g.2.0100
+1
31.03033.0301
41.04064.0604
51.05105.1010
The FVIFA is the portion of Formula 2.8 which appears in brackets. Using Table B to
calculate the FVA therefore requires only the product of the instalment and the Table B
FVIFA which for our example is as follows:
FVA = PMT × FVIFAn;r
= R100 × FVIFA3;12%
= R100 × 3.3744
= R337.44
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FINANCIAL MANAGEMENT
Similar principles to those already developed for dealing with a single amount investment
can be used to determine the rate or number of periods as well as for more frequent
compounding.
Series of investments, annuity due
Where specifically stated, an annuity may be structured by depositing the first instalment at
the beginning of the period. Such an annuity is known as an annuity due. Because Table B
has been compiled for ordinary annuities, certain adjustments need to be made if an annuity
due accumulation factor is required. In our example, we can have a three year annuity of an
equal payment which occurs at the end of each period, or an equal payment which occurs at
the beginning of each period.
Example 2.10: Calculating the future value of an annuity due
An investor pays an instalment of R100 at the beginning of each year into a savings account
yielding 12% per year interest compounded annually. What is the future value of the
investment at the end of three years? It is useful to use a diagram of cash flows to develop
the relevant formula.
Table 2.3 Future value of an annuity due at 12%
Year end
Instalment
0
R100
1
2
R100
R100
3
(1.12)1
R112.00
(1.12)
R125.44
(1.12)
2
R140.49
3
Future value of annuity due = R377.93
In this case all three instalments earn interest. We could undertake three separate
calculations and sum the results. In order to adjust the Table B reading, an annuity due
requires the reading under 3 + 1 periods, but without the first instalment. The table reading
is thus adjusted by adding one period, that is, by reading under four periods rather than
three periods and then deducting one from the factor indicated by Table B. This converts
the table reading to reflect investment at the beginning of a period rather than the end of
the period as follows:
FVA = PMT × (FVIFA(3 + 1); 12% – 1)
= R100 × (4.7793 – 1)
= R377.93
The formula for the future value of an ordinary annuity, Formula 2.8, can similarly be
adjusted for an annuity due as follows:
[(
) ]
(1 + r)n + 1 – 1
​  ​– 1 ​(Formula 2.9)
FVAdue = PMT ​ ​ 
​
r
[(
) ]
(1 + 0.12)4 – 1

​ ​– 1 ​
= R100 ​ ​
​
0.12
= R377.93
It is possible to multiply our solution from applying Formula 2.8 by (1+r/m) to arrive at the
same solution1. In our example (see previous page), R337.44 × (1+0.12/1) = R377.93.
1
We are grateful to Colin Smith for making this point.
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2-13
An annuity due will have a higher future value than an ordinary annuity because the investment
is made earlier, which means that each instalment will earn interest for an additional period.
Future values when the timing of the cash flows and the compounding periods
differ
So far, to use the formulae, and financial calculators, we have had a cash flow per period and
an interest rate for the same period. Therefore, if there are quarterly payments, interest is
compounded quarterly. What do we do when there may be quarterly payments but interest is
compounded monthly? For example, a company deposits R10 million per quarter for 5 years
and interest is 6% per year, compounded on a monthly basis. One way is to determine the
effective interest per quarter and apply this in our calculations of future value. The monthly
rate is 0.5% [6%/12] and there are 20 quarters.
Effective quarterly rate = (1.005)3 – 1 = 0.015075
[
]
(1+ .015075)20 – 1
​  ​
FVA = 10m × ​ 
​
0.015075
= R10m × 23.14075
= R231.41m
2 PRESENT VALUES
Present value is a powerful concept in finance. If you receive money today, you can invest
it to earn interest. This means that you will prefer to receive R100 today rather than R100
in a year’s time, as you can invest it and earn a return. Up to now we have wanted to know
what the future value will be in, say, five years’ time if we invest, say, R100 today. For
example, R100 invested for one year at 8% will result in a future value of R108. We now
turn the question around: how much do we need to invest today to reach a target of R108 if
the interest rate is 8%?
The present value, that is the value today, of a stream of expected future cash flows can
be established in much the same way as future values. Many valuation problems in financial
management involve calculating the present value of a stream of cash flows that is expected
in the future. Present value enables us to make direct comparisons between investments. It is
difficult, for example, to decide between alternative investments offering income streams which
may differ in the level of cash flows and the timing of such cash flows. For example, how do we
compare investments A and B with cash flows as set out in the following table? We can compare
the investments by determining the present value of the cash flows of each project, but more
about that later.
Project
0
1
2
3
A
-20
16
5
5
B
-20
1
5
23
Cash flows in Rm
The calculation of present values uses similar reasoning to the calculation of future values.
Instead of referring to compounding, we refer to discounting, which is the inverse of
compounding. The rate used to move cash flows back to the present is called the discount
rate. Why call this a discount rate? For example, if we purchase goods at a discount, we pay
less than 100% (1) of the price. You will notice that the factors in Table C are all less than 1
and this confirms that we are discounting back to today’s value.
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Single amount, single period, annual discounting
A rand today is worth more than a rand at a future time. This is the essence of the concept
of time value. Money received immediately is likely to be used productively and to be worth
more in the future.
Different individuals will generally have differing time-preference rates for money – that
is, they will apply different discount rates to future cash flows. These differences can be
attributed to the different needs or opportunities which would require them to make use
of the cash. The primary factors for determining an individual’s time-preference rate for
money, remain the time value of money, the risk attached to the investment, and inflationary
expectations.
Example 2.11: Calculating the present value of a future amount due in one year’s time
An investment offers the opportunity to receive R100 one year from now if R90 is paid
immediately. Should an investor who applies a 12% discount rate make the investment?
As present value is the inverse of future value, Formula 2.3 can be applied.
PV = 
​  FV n ​
(1 + r)
100  ​
= ​ 
(1.12)1
= R89.29
The present value of the investment to the investor is R89.29. As this is less than the cost of
the investment, of R90, it is not a worthwhile investment. One way of conceptualising this
outcome is to ask whether the investor would give R90 (the cost of the investment today)
in exchange for R89.29 (the value of the investment today). The answer is obviously no. In
much the same way as with future values, the formula can be adapted in order to determine
other variables if they are unknown.
Single amount, multiple periods, annual discounting
An amount of money to be received more than one year in the future clearly has an even
smaller present value than if it were to be received in a year’s time. Because interest rates
are compounded annually, the same principle is applied to discounting.
Example 2.12: Calculating the present value of a future amount due more than one year in
the future
An investment offers the opportunity to receive R100 in ten years’ time. If an investor
applies an interest factor of 12%, what is the highest price which will be offered for the
investment?
Applying Formula 2.3 the outcome is as follows:
FV ​
PV = ​  
(1 + r)n
100  ​
= ​ 
(1.12)10
= R32.20
The investor would therefore be prepared to pay any amount up to R32.20 for the investment.
If the required payment was R30, for example, the investor would purchase the investment
because it would be equivalent to paying R30 today and receiving R32.20 today.
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2-15
Formula 2.3 can also be written as:
[
]
1
PV = FV × ​ ​  
​  ​
(1 + r)n
[
]
= R100 × ​ 
​  1 10 ​  ​
(1.12)
= R100 × 0.3220
= R32.20
Table C reflects discount factors for all commonly used ranges of interest rates and periods.
It is referred to as the present value of R1 table, or PVIF, denoting that it provides the
present-value interest factor for a single sum to be received at a future date. It displays the
portion of the formula which is in brackets above.
Stream of cash flows, ordinary annuity (PVA)
A series of equal cash flows, the first of which is due at the end of the first period, is called
an ordinary annuity. In order to establish the present value of an ordinary annuity (PVA),
the future cash flows must be discounted to the present.
Example 2.13: Calculating the present value of an ordinary annuity
An investor wants to buy an annuity of R100 for the next three years. If a bank is prepared
to pay interest at 12%, how much must be invested today?
This is another way of asking what the present value of a stream of three annual payments
is. It can be illustrated as shown in Table 2.4.
Table 2.4 Present value of an ordinary annuity at 12%
Year end
0
1
2
3
Cash flowR100R100R100
R89.28
R79.72
R71.18
R240.18
1
(1.12)1
1
(1.12)2
1
(1.12)3
= Present value of the annuity
From Table 2.4 it is apparent that:
(
)
1  ​ + ​ 
1  ​  ​
PVA = R100 ​ 
​  1 1 ​ + ​ 
1.122 1.123
1.12
n
∑(
)
t
= R100 ​ ​​​​ 
​  1  ​  ​​ ​​
t=1 1.12
This relationship can be generalised and expressed in the equation:
n
∑(
)
t
PVA = PMT ​ ​​​​ 
​  1  ​  ​​ ​​
1+r
t=1
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FINANCIAL MANAGEMENT
It can be more conveniently expressed as follows:
(
)
1 – 
​  1 n ​
(1 +r)
​  ​(Formula 2.10)
PVA = PMT × ​ 
​
r
(
)
1 – 
​  1 3 ​
(1.12)
​  ​
= R100 × ​ 
​
0.12
= R100 × 2.4018
= R240.18
Again, the above formula is particularly useful when a specific rate or period cannot be
found in the tables.
A set of tables, referred to as the present value of an annuity of R1 per period, has been
compiled. Table D provides the present value interest factor for the annuity (PVIFA).
Reading from Table D, the solution should be:
PVA = PMT × PVIFA3;12%
= R100 × 2.4018
= R240.18
We can also use a financial calculator to solve these problems and do so in a separate section
later in this chapter.
In order to conceptualise what is happening in practice, follow Table 2.5.
Table 2.5 Ordinary annuity
An investment of R240.18 today earning an interest rate of 12% will enable an investor to
withdraw an equal payment of R100 each year for three years. This is a very powerful concept
in real world financial applications. For example, you may wish to invest now to be able
to withdraw a pension of R100 000 per year for three years. Equipment may cost R240 180
and a company borrows this amount and is required to repay the loan and interest in the
form of annuity payments of R100 000 each year.
Stream of cash flows, annuity due
A stream of cash flows may be structured in such a way that the initial payment is received
immediately rather than at the end of the first period. The calculation of the present value
of an annuity structured in this way requires an adjustment to the tables. Because the first
payment is received immediately, its present value is equal to its quoted value – that is, it
does not need to be discounted.
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2-17
Example 2.14: Calculating the present value of an annuity due at 12%
An investor wants to buy an annuity of R100 for the next three years, each instalment being
paid at the beginning of the year. If a bank is prepared to pay interest at 12%, how much
must be invested today?
It can be seen that the amount will be invested and the first instalment will immediately
be repaid. It can be illustrated as shown in Table 2.6.
Table 2.6 Calculating the present value of an annuity due at 12%
Year end
Cash flow
0
R100
1
R100
2
R100
3
1
R89.29
(1.12)1
1
R79.72
(1.12)2
R269.01
How does an annuity due relate to an ordinary annuity? The following diagram reflects this
relationship in terms of how we will restate the formulae and the tables.
If Table D is used it will be noted that the reading is exactly the same as if it were a twoyear annuity, but we need to add one to the present value factor because the immediate
instalment is not discounted. Using Table D:
PVAdue = PMT × (PVIFAn – 1; 12% + 1)
= R100 × (PVIFA2; 12% + 1)
= R100 × (1.6901 + 1)
= R100 × 2.6901
= R269.01
The present value of R269.01 for an annuity due can be compared with that of an ordinary
annuity calculated in Example 2.13 with a present value of R240.18. The annuity due has a higher
present value because the cash flows occur earlier than in the case of an ordinary annuity.
Formula 2.10 can be adjusted for annuities due as follows:
1
​
​  ​
1 – ​ 
(1 + r)n – 1 +1
PVAdue = PMT ×

​  ​
​ ​
​
​
r
= 100 ×
{[
{[
(
(
)]
)]
}
​  1 2 ​  ​
1 – ​ 
(1.12)
+1

​ ​
​ ​
​
​
0.12
}
(Formula 2.10a)
= R100 × 2.69005
= R269.01
We can also multiply our solution to Formula 2.10 by (1+r/m) to obtain the same value, so
that R240.18 × (1+0.12/1) = R269.01.
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FINANCIAL MANAGEMENT
What the formula is doing is reducing the number of discounting periods by one and
effectively adding [1 x PMT] to recognise that the present value of the first payment equals
its quoted value, as it occurs today.
In order to further conceptualise what is happening in practice, follow Table 2.7.
Table 2.7 Annuity due
Stream of cash flows, deferred annuity
A deferred annuity is an annuity which begins at some time in the future. This would occur if
an investor wanted to invest a sum of money now, but wanted the annuity to commence only
at some future date. An example of a deferred annuity is a pension plan.
Example 2.15: Present value of a deferred annuity
Let’s assume an investor wishes to invest a sum of money today which will yield three equal
instalments of R100, the first payable three years from today. If interest accrues at 12%, what
amount must be invested?
This is a present-value problem, requiring us to compute the value today of a stream of
future cash flows, the first of which is deferred. The cash flows can be illustrated as shown in
Table 2.8.
Table 2.8 Present value of an annuity deferred at 12%
Year end
0
1
2
3
Cash flowR100
R71.18
R63.55
R56.74
R191.47
1
(1.12)3
1
(1.12)4
4
5
R100
R100
1
(1.12)5
Table D is compiled on the assumption that the first cash flow arises at the end of period
one. Because of the deferred period, the table readings can easily be adjusted as follows:
PVA = 1 × (PVIFA5; 12% – PVIFA2; 12%)
= R100 × (3.6048 – 1.6901)
= R100 × 1.9147
= R191.47
The investment of R191.47 will earn interest for three years at the end of which the first
instalment of R100 will be paid out. The balance will earn interest for another year before
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2-19
the next instalment is paid out, and similarly for the third instalment. The amount of R191.47
is the amount which must be invested at period 0 to make the cash flows possible.
The following diagram indicates what is happening with a deferred annuity:
Figure 2.3 Deferred annuity
In the first three years, interest is earned until the end of Year 3 at a rate of 12%, when
the first withdrawal of R100 occurs. In Year 4, interest is earned on the balance of R169 so
that it will reach a level of R189 at the end of Year 4. After paying out another R100, there
remains a balance of R89, which with interest will grow to R100 by the end of Year 5, which
exactly equals the withdrawal of R100.
Uneven stream of cash flows
Companies will often be required to evaluate investments or projects which result in an
uneven stream of future cash flows. Further, cash flows may be negative in certain periods.
What do we do to determine present values in such cases? The annuity tables cannot be
used. Each cash flow must be treated separately and discounted using Table C: the present
value of R1. The present value of any cash flow can then be summed and the net present
value of the stream of uneven cash flows established.
Let’s go back to an earlier example. How do we evaluate Projects A and B?
Project
0
1
2
3
A
-20
16
5
5
B
-20
1
5
23
Cash flows in Rm
We are required to discount each cash flow. We will assume a discount rate of 10%. If we
add up the cash flows, Project A results in total cash flows of R26m, whilst Project B results
in total cash flows of R29m. Yet we have to wait longer for the cash flows of B. Let’s discount
each cash flow by applying the formula 1/(1 + r) n or by referring to Table C. Otherwise, you
can also use a financial calculator.
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FINANCIAL MANAGEMENT
Project
0
1
2
3
Cash flows in Rm
5
0.8264
4.1322
5
0.7513
3.7566
}
A
-20
16
PV Factor 0.9091
14.5455
Present Value 22.4343
If we do the same for Project B, the present value is R22.32m. This means that although
Project B has higher total cash flows, Project A has a higher present value of cash flows.
As the cost for both projects is equal, we would prefer to select Project A. We will use a
financial calculator to solve this problem later in the chapter.
Perpetuities
All annuities discussed so far have a finite life. The cash flows take place over a specific
time and then cease. There are cases of annuities which provide cash flows for an infinite
period. Such cash flows are called perpetuities. An example of perpetuity would be a nonredeemable preference share paying a fixed dividend.
Example 2.16: Calculating the present value of a perpetuity
An investor wants to buy 1 000 non-redeemable 9% preference shares of R1 each. If the
interest rate which he applies is 12%, what is the present value of the investment?
In essence the investor is buying a future cash flow in perpetuity amounting to 9% of
R1 000, that is R90. Because a 12% return on the investment is expected, this problem
requires the principal sum to be determined.
PV = 
​ PMT
r ​(Formula 2.11)
90  ​
= ​ 
0.12
= R750
The cash flow in perpetuity of R90 represents a return of 12% on R750. The investor who
requires a return of 12% will therefore be prepared to pay no more than R750 which is the
present value of the investment.
Let’s relate the formula of perpetuity to that of an annuity. We determine the present value
of an ordinary annuity by applying the following formula:
1 – 
​  1 n ​
(1 + r)
PVA = PMT
​  ​
​ 
​
r
As n approaches infinity, 1/(1 + r)n approaches zero and the formula becomes PMT × 1/r,
which is the perpetuity formula.
[
]
Growing perpetuities
If a cash flow is growing at a constant rate, then we call this a growing perpetuity and this is
a very useful concept in valuing companies, and so we will return to this in a later chapter
in another guise. The following could be a future cash flow stream which is discounted at a
given interest rate, r.
PMT2
PMT3
PMT1
​ + ​ 
​ + ..............
PV = 
​
2 ​ + ​ 
(1 + r)
(1 + r)
(1 + r)3
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2-21
If the payment is growing at a steady rate, then we can use the payment just made, PMT0,
and apply the growth rate and so the formula becomes:
PMT0(1 + g)

​
(Formula 2.12)
PV =
​
(r – g)
We will come back to this in a later chapter and will explain the derivation of this formula
in greater detail.
If a company has just made a payment of R10 million and this is expected to grow at the
expected inflation rate of 3% per year and the discount rate is 8%, then the present value
of this payment stream is:
10m(1 + 0.03)
_____________
PV =
​     ​= R206 million
(0.08 – 0.03)
Growing annuity
If an amount is growing at a constant rate for a specified number of years, then we can use
the following formula to determine the present value rather than discounting each cash
flow.
[
]
(1 + g)n
1 – ​ n ​
(1 + r)
PV of a Growing Annuity = PMT (1 + g) ×
​  ​
​ ​ 
r–g
(Formula 2.13)
Assume that you have just graduated and you are expecting an annual salary of R360 000
(today’s value) which you expect to grow at a rate of 6% per year for the next 40 years, at
which time you will retire. What is the present value of your future salary over your working
life if your required return is 9% per year? Assume an annual salary payable once a year.
[You can easily change this by using monthly rates and your monthly salary.]
[
]
(1.06)40
​
1 – ​ 
(1.09)40 = R8 554 551
PV of a future salary = R360 000 (1 + 0.06) ×
​ ​    ​
0.09 – 0.06
This means that the present value of your future salary earned over 40 years is just over
R8.5 million. This is before taking into account such issues as taxation which will reduce the real
worth of your future salary. We are assuming that your first year’s salary will be R381 600.
We can do these calculations the “long” way by using Excel spreadsheets. Invariably this
is how it is done in practice and we will show you later how to use Excel spreadsheets to
solve time value of money problems.
Inflation and real returns
The effect of inflation is to reduce the value of money over time. Whilst investing in a bank
account may offer an interest rate of 4.8% per year, we need to consider the impact that
inflation will have on the purchasing power of money. If expected inflation is 3% per year
then you are not really making 4.8%. A R1 000 investment earning 4.8% will result in you
accumulating R1 048 by the end of the year. However, you will need R1 030 at the end of the
year for what you could have purchased for R1 000 at the beginning of the year. Obviously, this
will affect pension decisions as we may think that a pension of R30 000 per month is sufficient
but that is based on its current purchasing power. What will a pension of R30 000 per month
starting in 30 years’ time be able to purchase in relation to today’s prices? In other words,
what is the present value of R30 000 in 30 years’ time? Inflation of 3% per year amounts to
0.25% per month.
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FINANCIAL MANAGEMENT
[
]
1
PV = R30 000 × ​ 
​
​  ​
(1.0025)360
PV = R30 000 × 0.4070 = R12 210
This means that a pension of R30 000 in 30 years’ time will be able to buy only what R12 210
can buy today, and that is at the beginning of the retirement period. It is worse at the end.
The moral of the story is to include inflation in your investment calculations. A real return
refers to the return we make after deducting inflation. If an investment is offering 4.8% per
year and inflation is 3%, then the real return is approximately 1.8%. A more accurate way
of calculating the real return is as follows:
1 + real return = (1 + nominal return) / (1 + inflation rate)
We will come back to this again in a later chapter.
3 SOME REAL WORLD APPLICATIONS
Retirement planning
Time magazine ran a cover which read: “Will you EVER be able to RETIRE?” This
explored the effect that lower returns would have on the retirement prospects of millions of
Americans. In South Africa, the combined effects of people living longer lives, low interest
rates and lower expected future returns from the share market, mean that the economy
will not be able to afford to pay old age pensions and retirees will not have accumulated
sufficient amounts in their pension funds to retire comfortably. This issue is compounded by
the low savings rates of South Africans. A few years ago, a Business Day editorial indicated
that only 6% of South Africans would be able to retire without experiencing a reduction
in their standard of living. Referring to an Alexander Forbes survey, the editorial stated that the
average employee will retire on a pension equivalent to 28% of his/her final salary. Employees
are contributing less than 10% of their salary to their pension fund whilst Old Mutual reported
that employees should contribute 15% of their salary over 40 years in order to maintain their
standard of living on retirement.
Time value of money principles are critical in retirement planning. Whilst the last thing
on your mind may be retirement, it will affect your parents, and the earlier you start the better
off you will be. Increasingly there are careers in financial planning and managing pension
and retirement funds. So, how can we apply time value of money principles to retirement
planning?
It is useful to be able to determine the single sum investment or the annuity required
to provide adequately for retirement. To achieve this, an investor must estimate the length of
time prior to retirement, the return that will be earned on the funds invested during and after
this period and, finally, the amount of funds required for retirement.
As most investors are not in a position to invest single lump sums, retirement plans are
generally structured to require monthly contributions from the investor. On retirement, the
investor will usually receive a pension which is in the form of an annuity.
Example 2.17: Calculating the required contribution to a retirement fund
Kate Smith wishes to retire in 30 years’ time and has estimated that she will require a
monthly pension income of R24 000 per month for 20 years subsequent to retirement. Kate
will contribute to a retirement fund which will enable her to take out a monthly pension of
R24 000 after retirement. The retirement fund is currently earning a return of 9% per annum,
interest compounded monthly, and this level of return is expected to remain unchanged and
to be sustainable over the next 50 years. Determine the monthly contribution that Kate is
required to make to the retirement fund over the next 30 years.
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THE TIME VALUE OF MONEY
2-23
First we need to calculate the present value required at retirement date to generate an
annuity of R24 000 per month for 20 years. The interest rate is 0.75% per month (9%/12)
and there are 240 months (12 3 20). The “present value” of the pension in 30 years’ time is
established as follows:
[
1
1 – _________
​
240 ​
]
(1.0075)
PV = 24 000 × ​​ _____________
​  ​
​
0.0075
= 24 000 × 111.14495
= R2 667 479
This is the present value of the amount required to sustain a monthly payment of R24 000
for 20 years. This is the amount that she needs to accumulate in 30 years’ time to be able to
purchase an annuity or pension of R24 000 for 20 years after retirement.
The monthly contribution required over the next 30 years to generate an accumulated sum
of R2 667 479 is calculated as follows:
[
]
(1.0075)360 – 1
R2 667 479 = PMT × ​ 
​  ​
​
0.0075
= PMT × 1 830.7435
PMT = R2 667 479/1830.7435 = R1 457.05 per month
Of course, the above solution assumes that we are able to predict the return the fund will
earn and the amount required at retirement age. In practice this is often very difficult as
factors such as inflation and future returns are largely unknown. However, the advantage of
such an exercise is that it gives us an indication, based on certain assumptions, of the level
of investment required.
Let’s see what happens when three very realistic events occur: people live longer, start
saving later and the returns on retirement funds are expected to be at lower levels in the
future. What happens to the required monthly payment if the expected lifespan after
retirement is 30 years, returns have fallen to 6% per year and Kate starts saving only 20 years
before retirement? Do the workings and you will find that Kate will need to have accumulated
R4 002 999 by retirement date and this translates into a monthly contribution of R8 663.73 per
month for the next 20 years. This is almost 6 times the figure of R1 457.05 with our previous
assumptions. So it is easy to understand why there are corporate pension plans under water
and unhappy retirees, although I am sure they are not complaining about living longer lives.
Governments will find it difficult in the future to afford the payment of adequate old age
pensions and the government is promoting later retirement. Increasingly we will see older
people doing part-time work to supplement pensions. The pension crisis is on the horizon,
so plan early. We will analyse retirement planning, inflation and living annuities in greater
detail in Appendix 2.1.
Loan amortisation schedules
There are many real world applications of the repayment of loans on the basis of equal
instalments over a number of years. What are some of the applications that will affect
you now and in the future? Firstly, you may need to repay a student loan on the basis of
instalments. You will purchase a car and may need to repay the car financing loan on an
instalment basis. Also, you may purchase residential property which requires that you repay
a mortgage loan over 30 years in monthly instalments.
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FINANCIAL MANAGEMENT
Let’s firstly assume the following example.
You have purchased an old but beautiful red Alfa Romeo for R100 000. The dealer has
given you a car loan at an interest rate of 7% per year, interest compounded annually and
repayable in equal instalments over 5 years. What is the annual instalment?
[
]
1  ​
1 – ​ 
(1.07)5
​  ​
R100 000 = PMT × ​ ​  
0.07
PMT = R100 000/4.1002
= R24 389.07 per year
This can be broken down into payment of interest and principal and set out in a loan
amortisation schedule as in the following table.
Table 2.9 Loan amortisation
The first instalment of R24 389.07 is made up of R7 000 of interest (R100 000 × 7%) and
a repayment of principal of R17 389.07. The balance at the end of the year is R82 610.93
(R100 000 – R17 389.07). The second instalment at the end of the second year includes
interest of R5 782.77 (R82 610.93 × 7%) and a repayment of capital of R18 606.30. The
interest component falls over time as the capital amount is reduced to zero by the end of
the 5th year.
Mortgage loan
Assume that you have set your heart on an apartment that is 5 minutes from the beach and
the price is R2 million. You have managed to obtain a 100% mortgage loan from the bank
at an interest rate of 7.2%, interest compounded monthly, which means that you will be
charged a monthly interest rate of 0.6%. The term of the loan is 30 years i.e. 360 months.
What is your monthly repayment on the mortgage loan?
​[
]​
1
​
1 – 
​
(1.006)360

​  so PMT = R2 000 000/147.3214
R2 000 000 = PMT ×
​
0.006
= R13 575.76 per month
If we draw a graph of the mortgage loan amortisation schedule over 30 years, it will indicate
the balance of interest and the amortisation of the mortgage loan. The principal component is
relatively small but increases over time. This can be quite disheartening in the first few years.
For example, of the first month’s instalment of R13 575.76, the interest component is R12 000
and only R1 575.76 will be allocated to repaying the R2 million loan. A monthly instalment of
R13 575.76 over 30 years will result in the repayment of the R2 million loan and interest. So
how much interest will be paid over the term of the mortgage loan?
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THE TIME VALUE OF MONEY
2-25
Figure 2.4 Loan amortisation
If we multiply R13 575.76 by 360 months, we find that the total amount paid is close to
R5 million (R4 887 274) and so total interest amounts to R2 887 274. That is quite a sum
and so next time someone tells you that he purchased an apartment for R2 million and sold
it for R5 million, the sums are a little more complicated than they seem. There are costs
such as maintenance and you have to live somewhere so take off the rent you would have
had to pay.
4 FINANCIAL CALCULATORS AND SPREADSHEETS
Using financial calculators
Financial calculators are programmed to compute future values and present values and
other related variables. Financial calculators require you to enter the data using the relevant
Input keys which for the HP-10BII are as follows:
What do these keys mean?
N = number of periods
I/YR = interest rate as a percentage
Enter a number, so if the rate is 10%, enter 10, not 0.10. Other calculators may reflect the
interest rate per period as [i] and the number of periods as [n].
PV = present value
PMT = annuity payment (Specify this as a zero when working with single sums only.)
FV = future value
In most cases, three or four inputs will be specified, and the financial calculator will solve
for the remaining variable. On some calculators you will need to press the COMPUTE key
prior to pressing the missing input key.
What to watch out for when using a financial calculator
Outflows are recorded as negative cash flows. An investment will be recorded in present
value terms as a negative amount. If you borrow, you will receive the loan amount today
which will be recorded as a positive cash flow and the repayments will be reflected as
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negative amounts. Ensure that you clear the memory. Enter a zero for any variable that is
not relevant in a particular case. For example, when determining the future value of a single
sum investment, enter a zero for the PMT key.
Ensure that the financial calculator is programmed for annual compounding by doing
the following steps:
Enter 1, then press SHIFT key and then the PMT (P/YR) key. We will make adjustments
later for non-annual compounding.
Let’s do some of the previous examples by using an HP-10BII financial calculator.
An investment of R100 invested for 10 years earning 12% per year compound interest will
result in a future value of R310.60. Key in the following input values and press the FV key
for the solution.
First enter the present value as a negative number, –100 or press 100 followed by (–),
depending on the calculator being used, and then press the PV key. Then enter 10 and press
N, enter 12 and press I/YR, enter 0 and press PMT and then press FV (or Comp FV) to find
the answer.
If given a FV of 310.6 with the number of periods being 10 and an interest rate of 12%,
then key in the following variables and press the PV key to find the answer of –100:
What is the interest rate that will achieve a present value of R100 growing to R310.60 within
10 years? Enter the inputs, then press the [I/YR] key to determine the interest rate of
12%.
We have assumed so far that the company has annual compounding. If the compounding
period is less than a year, then we will need to input the number of compounding periods per
year. This requires us to press the number of periods per year, then press the SHIFT key and
(P/YR).
Let’s go back to the first example and assume monthly compounding. We need to program
the financial calculator for monthly compounding by undertaking the following steps:
Enter 12, and then press the SHIFT key and then the PMT (P/YR) key.
This means that the financial calculator is now programmed for monthly compounding. The
present value is R100, the interest rate is 12% per year and N is 120 months.
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Remember to input the annual interest rate. The financial calculator will divide it by the
number of compounding periods per year. The effect of compounding interest each month
rather than each year is to increase the future value from R310 to R330. Remember to input
the number of months.
Present values
What is the present value of an annuity of R100 per year for three years at an interest rate
of 12%?
The present value is R240.18. This assumes that the annuity occurs at the end of each year.
What is the present value of an annuity that starts at the beginning of each year? Firstly,
set the calculator to the beginning of year by pressing the SHIFT key and press the BEG/
END key. Then enter PMT of –100, N of 3, I/YR of 12, FV of 0 and then press PV to find
the answer of R269.
Remember to reset your financial calculator back to end of period mode by pressing the
SHIFT key and the BEG/END key. Usually we will assume that cash flows occur at the end
of each period. Remember always to ensure that you clear the memory and all previous
inputs by pressing the SHIFT key and then the C ALL key.
How do we use a financial calculator to determine the present value of an uneven stream
of cash flows? We will use the CFj and the I/YR keys to input data and press the NPV key
for the answer. Let’s assume that Project A has the following cash flows:
YR
1
2
CF Rm
16
5
3
5
Assume there is no cash flow now today, i.e. time zero. You will still need to input a value,
so enter zero. Firstly, input 0 then press the CFj key, then input 16 and press the CFj key,
input 5 and press the CFj key, input 5 and press the CFj key, input 10 and press the I/YR
key and then press the SHIFT key followed by pressing the NPV key to find the answer of
R22.4343m.
Using Excel spreadsheets
Although financial calculators can be very useful, in practice managers will prefer to use
Excel spreadsheets to solve time value of money problems. Excel is a very powerful tool
in many applications of corporate finance and useful in financial modelling. Like financial
calculators, Excel has many built-in time value of money functions, yet it goes further as it
allows us to obtain a visual perspective and permits us to put cash flows on a time line by
using a cell to reflect a time period. It also allows us to build financial models so that we can
see the effect of changing variables without redoing the whole calculation.
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We place the relevant values in cells. Although this is not necessary as we can use Excel as
a financial calculator, it does represent best practice as it enables us to undertake sensitivity
analysis. Values are therefore anchored in cells and when we change the value in a particular
cell the answer will change. We will use Excel to solve a few time value of money problems.
What is the future value of R10 000 invested today for 20 years at an interest rate of
6% interest compounded annually? In Excel we will place these values within cells. In our
example there are no annuity payments and so the type (beginning of period =1, end of
period =0) is not relevant. We have used Cell B8 to place the Future Value function which
is; =FV(rate, nper, pmt, PV, type). We place the rate in Cell B6, and the number of periods
is placed in Cell B5. The PV is placed in Cell B3. The payment (pmt) is placed in Cell B4
and type is placed in Cell B7.
The objective is to calculate the future value and so we type the Excel Future Value function
in Cell B8, which in this case would be: =FV(B6,B5,B4,-B3,B7). The answer of R32 071
appears in the cell. What this means is that we can now change each variable and see what
happens to future value. For example, if we expect that the interest rate will be 10%, then
place this in Cell B6, and the answer in Cell B8 will now indicate a value of R67 275.
Let’s use Excel to determine the present value of an ordinary annuity of R7 000 per year
for 5 years at an interest rate of 6% per year. We will use the same Excel function but we will
use a separate worksheet. Insert R7 000 in Cell B3 as the payment and 6% in Cell B4 as the
discount rate. We will place 5, being the number of payments, in Cell B5. The future value is
zero and we place this in Cell B6 and place a 0 for type in Cell B7, to indicate that this is an
ordinary annuity. This means that the annuity payment is received at the end of each period
and starts in this case, in a year’s time. In Cell B8, we insert the Excel function, =PV(rate,
nper, pmt, FV, type) and refer to the relevant cells where these variables have been placed.
The answer is R29 486.55.
What is the present value if the annuity was an annuity due? If this is the case, then simply
change the value of Type, B7, to 1. The present value indicated in Cell B8 will increase to
R31 255.74.
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The main functions in Excel to solve time value of money problems are:
Future Value:
Present Value:
Interest rate:
Number of periods:
Payment:
= FV (rate, nper, pmt, PV, type)
= PV (rate, nper, pmt, FV, type)
= RATE (nper, pmt, PV, FV, type)
= NPER (rate, pmt, PV, FV, type)
= PMT (rate, nper, PV, FV, type)
There are many other functions that you can use but we have limited this to the above for
now. In most cases you can omit the type or indicate a zero. Excel indicates which variables
are important to enter.
In Excel we can also set out the cash flows in Cells with each cell indicating a time period.
This is particularly useful for determining the present value of uneven cash flows, but we
can use it also for any type of cash flow. We then use the =NPV function which will discount
the future cash flows at a specified discount rate. Remember that the NPV function assumes
that the first cash flow occurs in one period’s time from today.
The NPV function in Excel requires us to indicate the discount rate and the RANGE of
cash flows to be discounted and will assume that each cell represents a period. We simply
indicate in a Cell =NPV(rate, range). In the following example, the discount rate has been
placed in Cell E3 and the cash flows have been placed in Cells C5 to G5. Therefore in Cell
B7, you will type =NPV(E3, C5:G5) and the answer will indicate R29 486.55.
If we are discounting a series of cash flows which commence today, then we should indicate
the range that should be discounted, in this case C11 to F11 and then add today’s cash flow
at today’s value. In reality we are discounting the cash flows in periods 1 to 4 by using the
NPV function and adding to this the value of Cell B11, which is R7 000.
The NPV function is very useful for discounting a series of uneven cash flows.
We will come back to the use of Excel spreadsheets in later chapters. We have just touched
the surface in terms of using spreadsheets to solve corporate finance problems.
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5 THE ROLE OF INTEREST RATES
When we borrow money, we need to pay for the use of these funds. This is interest and the
interest rate is normally indicated as a percentage of the amount borrowed, which is called the
principal amount. A company may borrow to invest in plant and equipment and is prepared to
pay for the loan because the use of the borrowed funds is expected to generate a value greater
than the cost of borrowing. The bank lending the funds to the firm will lend at a rate that is
higher than the cost of such funds to the bank. The bank may be borrowing from other banks,
its depositors, the South African Reserve Bank or from the issue of bonds. Supply and demand
for funds will drive interest rates, although the South African Reserve Bank can influence
short-term interest rates by setting the “repo” rate, which is the interest rate that banks borrow
from the South African Reserve Bank.
In general, the interest rate, which represents the return required by the lender, is
influenced by three main variables. They are:
■■ The time value of money. People prefer to receive money sooner rather than later. This
principle arises because money can be invested to earn more money. Thus the earlier
cash is received, the greater is the potential for increasing wealth.
■■ The risk of the capital not being repaid. If there is some uncertainty that the capital amount
will be repaid, a premium will be required. When there is a high degree of certainty,
for example in the case of loans to the government in the form of treasury bills, bonds
or other “gilt” investments, the premium will be low. This is consistent with the most
fundamental principle in financial management: that return must be commensurate with
the risk taken.
■■ Inflation. In times of rising prices it is evident that the purchasing power of money
decreases over time. Any lender would expect to be compensated for this decline in
purchasing power. If the interest rate did not compensate for inflation the lender would
be poorer when the capital is repaid than at the time of the loan.
Liquidity will also impact on the interest rate. If a security is liquid, then it can be converted quickly
into cash at a realistic or fair value. Investors will demand a liquidity premium if a company’s
bonds are not liquid. The lack of liquidity was an important factor during the global financial crisis.
The rate of interest does not remain constant but depends on expected changes in
these variables. Figure 2.5 represents a typical yield curve which reflects the ruling interest
rates on investments maturing at various times in the future. The term structure of
interest rates, as it is called, reflects the rates of interest charged at any given time for
borrowing over different periods, from short-term to long-term. It seems reasonable to
expect that longer-term loans carry more risk than short-term loans, so we would expect to
see an upward-sloping curve. If this is coupled with the expectation that inflation rates are
likely to escalate in the future, an upward slope such as that in Figure 2.5 would result.
14
12
10
8
6
4
Figure 2.5 Typical yield curve
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So what is the yield curve in South Africa? This is also called the term structure of interest
rates. Yields quoted for RSA Government Fixed Coupon bonds on 10 May 2018 were as
follows and we can plot a yield curve to depict the term structure of interest rates.
Table 2.10 South African Government Bond Yields
Government bonds pay varying coupon interest rates. A coupon rate of 10.5% for the R186
issue means that the South African government will pay investors R10.50 per year on a R100
bond. This is normally paid semi-annually, so an investor will receive R5.25 per R100 bond
every half year. The coupon rate stays fixed at 10.5%. However, the price that this bond
is trading at means that investors will receive a yield of 8.5% per year. The R186 will be
redeemed in 3 instalments on 21 December 2025, 21 December 2026 and 21 December 2027
when the par value of R100 will be repaid to investors. If we plot these yields, we can see
that generally the yield curve in May 2018 is upward sloping.
Figure 2.6. Yield curve in South Africa
A number of theories have been developed to explain the term structure of interest rates.
The most commonly quoted theories are the expectations theory, the liquidity preference theory
and the market segmentation theory. We can also refer to the precautionary motive for holding
liquid or short-term assets.
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The expectations theory
Assuming an investor is faced with the choice of investing a sum of money for one year in a bond
at a fixed interest rate, or for five years in a five year bond. Which alternative will be chosen? If
it is expected that interest rates will decline during the next five years, it will be better to invest
for five years as a higher interest rate will be obtained from the investment than if a series of
five one-year investments had been made. If this expectation of generally declining interest
rates was held by all investors, then the five-year investment would be in greater demand if
offered at the same rate as the one-year investment. This demand would force the rate of the
five-year investment down, until both alternatives would be equally attractive.
This leads to the question of which factors are likely to contribute to expectations
relating to the increase or decrease in interest rates on bonds. The expected inflation rate
is a significant factor. An investor would clearly hope at the end of a year to be at least as
wealthy as the result of an investment as at the beginning of the year. The interest received
should therefore at least compensate for the loss of purchasing power as a result of inflation.
In fact, as most interest received is taxable, the investor would expect the after-tax interest
to at least compensate for inflation. In essence, the expectations theory holds that the slope
of the term structure of interest rates depends on the expected future spot rates of interest. If it is
expected that future rates of interest will be higher, the yield curve will be upward-sloping.
The liquidity preference theory
A second theory which attempts to explain the term structure of interest rates introduces
an element of risk. When dealing with investments such as government bonds, the risk is not
related to default on the capital invested, but rather to interest rate fluctuations. For example,
assume you hold both a 6-year RSA Government and a one-year RSA Government Bond,
each with a face value of R100 and each with a coupon rate of 8%, when the market rate of
interest is also 8%. If the market interest rate rises, the negative effect on the value of the
6-year RSA Bond would be far greater than on the one-year RSA Bond. The interest rate
risk is greater, the longer the period to maturity. Figure 2.7 illustrates the effect of changes
to the market interest rate on the price of two 8% RSA Bonds with differing maturity dates.
Figure 2.7 Value of 8.0% RSA Bonds on 1 October 20x6
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As these investments are RSA Bonds, the risk of default on repayment is virtually zero.
However, there is considerable risk for the longer-term bond if market interest rates
increase. If the market rate on 1 October 20x6 is 8%, the value of both bonds will be
the same at R100. If the market interest rate rose on that date to 11%, for example, the
value of the 6 year Bond would decline by R12.69(100.00 – 87.31) considerably more
than the decline in value of the 1 year Bond due at the end of September 20x7, of only
R2.70 (100.00 – 97.30).
The reasons for the greater variability of the 6 year bond stems from the difference in
the timing of the cash flow between the two investments. Investors holding the 6 year bond
are locked into receiving a 8% return on R100 for 5 years longer than holders of the 1 year
bond.
As investors prefer certainty to uncertainty, the theory holds that investors will generally
prefer short-term investments to long-term ones. As a result the short-term rates will tend
to be lower than long-term rates because of the higher demand for short-term investments.
However, short-term bonds are exposed to reinvestment rate risk. When we need to reinvest
maturing short-term bonds (“rolling-over”) then we are uncertain what the interest rate will
be at the time.
The market segmentation theory
The market segmentation theory is based on the premise that different investors have
differing investment preferences as to timing due to legal, regulatory, business and personal
motives. Life insurance companies and pension funds have long term liabilities and prefer
to invest in securities which have distant maturity dates. Banks may invest in short-term
securities as most of their liabilities are of a short-term nature. This theory implies that
interest rates are determined by demand and supply factors in these market segments.The
other factor is that the Reserve Bank will have a greater influence over short-term rates
rather than long term rates.
6 APPLYING THE TIME VALUE OF MONEY PRINCIPLES TO BONDS
The principles of the time value of money are applied in the valuation of bonds. A bond
is a financial instrument issued by government and companies to raise funds. The bond or
debenture will stipulate that the issuer is obliged to pay the bond holder a fixed interest or
coupon rate until the maturity of the bond when the capital amount, usually R100, will be
repaid to the bond holder. The bond document is a negotiable instrument, meaning that
it can be traded during its life span by investors wishing to buy or sell bonds. The name
dates back to earlier days when the bond certificate had attached to it, a series of coupons,
which entitled the bondholder to collect the interest by surrendering each coupon on the
due date.
A Treasury bond is in fact a loan to the government for a number of years. The name of the
bond is the RSA Government bond; the annual interest rate payable may be 7.5% (the coupon
rate); the year in which the capital amount of the loan will be repaid may be 2023 (the year of
maturity). An investment in a bond is thus the purchase of a stream of expected cash flows.
The cash flows are virtually certain, given the credibility of the issuer of the bond, and are thus
considered to be a low risk investment. Investment in bonds are most typically made by large
pension funds, to ensure that the fund has an allocation of low risk investments with a certain
interest cash flow to the fund.
The terminology and valuation procedures relating to bonds and bond portfolios are
complex and detailed coverage is not undertaken here. We will focus on applying the time
value of money principles we have studied so far.
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■■
■■
■■
■■
■■
■■
FINANCIAL MANAGEMENT
A bond is a financial instrument offering two distinct cash flows. Firstly, it offers
a stream of regular cash flows in the form of coupon payments. Using time value
principles, this is identical to annuity cash flows on regular, equally spaced time periods
in the future. Secondly the repayment of the nominal value will occur on maturity date.
Using time value principles, this is the equivalent of a single sum payment at a determined
future date.
An investor who purchases the bond and holds the bond to maturity has a high degree
of certainty that each coupon amount of R3.75 will be paid twice a year (semi-annually)
on the specified dates, and that the face value or par value will be returned on maturity
date. The investor will thus receive a coupon return of 7.5% per year.
Bonds may be bought and sold during the period from issue to maturity. It is not
uncommon for a bondholder to sell a bond to a willing buyer, who wishes to hold bonds
at a time when a new issue is not available.
The selection of the coupon rate is dependent upon economic factors at the time of
the issue. Prevailing interest rates, inflationary expectations and the expected return of
investors from bonds in a similar risk category are the most important factors. These
determine the required rate of return of investors in bonds. The required rate of return
is also referred to as the Yield to Maturity (YTM).
Even more significant in understanding what follows, is the awareness that interest rates
in the economy may change during the life of the bond. Such changes will impact on the
YTM, and therefore on the value of the bond. Note, however, that if the bondholder
simply retains possession of the bond, the return to the bondholder over the life of the
bond will be 7.5% per year.
There are consequently three variables that impact on the value of a bond. They are
firstly the coupon rate at which the bond was issued, secondly the ruling market rate
in the economy at the time of valuation, which is reflected in the required YTM, and
thirdly the period of time remaining to maturity.
We are now in a position to explore the valuation of bonds. We will value an RSA Government
security which has a fixed coupon rate of 10% per year, and a face value of R100. Coupon
interest is payable semi-annually and the maturity date is the end of October 2023. Assume
the current date is 1 November 2019. The current market yield (yield to maturity) on similar
securities is 8% per year (4% per half-year)2. What is the value of this RSA Government
security? The future cash flows from investing in this security can be depicted as follows:
The discount rate to apply to the future cash flows will be 4% per half-year (8%/2). We will
assume that the cash flows will occur at the end of April and October of each year.
The valuation of the bond can be done in two steps using the principles of present value
calculation. Step 1 entails discounting the coupon cash flows, which are an annuity, using
Formula 2.10. Step 2 entails discounting a single sum, the nominal value to be received on
maturity date, using Formula 2.3.
In terms of market convention, we quote rates on an annualised basis (interest rate per period × number of
periods in a year). This is not the effective annual rate, which is (1.04)2 = 8.16%.
2
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Step 1: Present value of an annuity of R5 for 8 periods at 4% per half-year.
[
]
1 – 
​  1 8 ​
(1.04)
​  ​
PVA = PMT × ​ 
​
0.04
PVA = R5 × 6.7327
= R33.66
Step 2: Present value of a single amount of R100 to be received in 8 periods’ time at
4% per half-year.
PV = R100 3 0.7307
= R73.07
Sum of two streams of cash flows = R33.66 + R73.07
= R106.73
We can also use the present value factors for each cash flow and then sum the present values
to obtain the value of the bond. Otherwise, use the NPV function in Excel to discount the
future cash flows at 4% per period.
The value of the bond is trading at a higher value than par because investors are requiring a
return of 8% per year (4% per half-year) and the bond is offering a coupon rate of 10% per
year (5% per half-year). A price of R106.73 means that investors will receive a return of 8%
per year (4% each half-year) until maturity. If market interest rates rise to 12%, then the
value of the bond would fall to R93.79, which is below par as the bond is offering only 10%
per year whilst the market is offering at 12%. At a price of R93.79, investors will receive a
return of 12% per year (6% per half-year). If the market interest rate is 10% per year, then
the market value should equal the par value of the bond. If we redo the valuation at 10%
(5% per half-year) we will see that this is true.
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A useful point to note here is that investors and bond portfolio managers aim to forecast the
timing and magnitude of interest rate changes in the economy. It is evident that if a fall in
market interest rates is correctly forecast, the purchase of bonds prior to that date will result
in a significant capital gain on sale, after the YTM responds to the rate fall.
We have seen a fall in market interest rates (and inflation) over the last 15 years in South
Africa, and interest rates in the USA and Japan have been at historically low levels. Also
refer to the South African Reserve Bank website (www.resbank.co.za) for more information
about interest rates. The fall in interest rates has resulted in a rise in bond values over this
period.
We saw in a previous example that the price volatility increases with the term to maturity.
Therefore the value of a 5-year bond will change to a greater extent than a 1-year bond.
However, the price volatility is also linked to the coupon rate. The lower the coupon rate
the more volatile will be the changes in price to changes in interest rates. This simply reflects
the fact that you can reinvest the coupon payments at the market rate. A composite measure
of term to maturity and coupon is called a bond’s duration and the greater the duration of a
bond, the more sensitive a bond’s value will be to changes in market interest rates.
The following principles summarise the use of time value principles and the impact on
bonds:
■■ A bond offers two cash flows – a series of coupon payments at a specified constant rate,
and the repayment of the nominal value of the bond at maturity.
■■ When the yield to maturity (YTM) differs from the coupon rate, cash flows are
discounted at the YTM in order to establish the present value of the bond.
■■ If the YTM moves above the bond coupon rate, the value of the bond falls below its par
value. If the YTM moves below the coupon rate, the value of the bond rises above its
par value.
■■ When the YTM differs from the coupon rate, the length of time remaining to maturity
of the bond impacts on the magnitude of the difference between the nominal value and
the market value.
■■ The longer the term to maturity, the greater the impact on present value. This was
graphically presented in Figure 2.7.
■■ Although not illustrated here, it also follows that if two bonds have different coupon
rates, the value of the bond with the lower coupon rate will change relatively more than
the bond with the higher coupon rate when the market YTM rises or falls.
■■ Finally, apart from the typical bond as described, bonds may come with other
characteristics. Bonds could have call options, which applies to some corporate bonds.
This allows the company to redeem the bonds at the option of the company, prior to
maturity date. RSA Government securities will pay coupons semi-annually (twice each
year). The cash flow line is thus constructed in periods of 6 months rather than annually.
Another example is a zero coupon bond, where there are no coupons. Only the future par
value, repayable on redemption date is therefore discounted to the present by the YTM.
We will now analyse bonds without a redemption date.
Perpetuals and 100-year bonds
A company (or country) may issue perpetual bonds which do not have a maturity date and
there is no obligation to redeem the face value of the bond. The company is required to make
the coupon interest payment forever. As there is no redemption of principal these bonds are
seen as more akin to equity. It is useful for banks to issue these types of bonds to bolster their
capital in terms of Basel III. Sukuk issues (a type of perpetual instrument) are popular in Islamic
countries and form a key component of Islamic finance as there is no redemption of principal
and therefore Sukuk issues may be viewed as equity. A perpetual bond’s value is simply:
Value = Coupon payment/market yield
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The value of a perpetual bond will be highly sensitive to changes in interest rates. If we use the
same example set out in Figure 2.7 (coupon 8%, principal R100), a rate rise from 8% to 11%
resulted in a fall in the market value of the one-year bond from R100 down to R97.30 whilst
the 6-year bond saw a fall from R100 down to R87.31. If this was a perpetual bond, then a 3%
increase in the market yield would see a fall in value from R100 to R72.73 [R8/0.11]
However, for investors expecting interest rates to fall, then the investment in perpetuals can
offer significantly higher returns. If the interest rate falls from 8% to 5%, then the increase in
value will be 60% for the perpetual bond, which is higher than the 15% increase for the 6-year
bond value and the 2.86% increase in the value of the 1-year bond.
Companies and countries have also started to issue 100-year bonds which are also highly
sensitive to interest rate changes but do have a redemption date. Just do not expect to get your
money back for you will probably not be around.
The advantages of perpetuals are that these bonds tend to offer a higher yield. However, it
is important to note that a number of perpetuals are callable by the company issuing the bonds.
This means that the company will have the right but not the obligation to redeem a “perpetual”
after a fixed period of time. For example, HSBC in Singapore issued 4.7% perpetuals which
are callable at par on 8 June 2022 and every 5 years thereafter.
Let’s come back to our example of an 8% perpetual bond but we will now assume that the
company can call/redeem the bond issue after five years. The company has the right to pay you
back but you cannot demand repayment of principal and simply have to sell the perpetuals if
you wish to recover the market value of the bond. If interest rates fell from 8% to 5%, then it is
highly likely that the company will call/redeem the bonds in five years’ time at par and reissue
new bonds at the lower rate of 5%. All this means is that when you value the bond, assume
that the higher coupon rate will only last until the call date if rates have fallen. If this happens
then this means that you are in effect valuing a redeemable bond with a likely redemption date
which is the call date.
If interest rates rise above the coupon rate, then the company will not call or redeem and
you can expect that you will receive the coupon payment forever which means that you will not
be able to reinvest your principal at the higher market rate. So, investors have downside and
limited upside as the company will call and refinance the bonds if market interest rates fall.
In exchange, the interest rate will be higher at least until the call date. Just do not expect to
receive the interest yield beyond the call date if market interest rates have fallen.
Example 2.18: Perpetual bonds, yield to call and yield to maturity
MTX issued perpetual bonds on 31 December 20x0 with a face value of R100 at a coupon
interest rate of 10%, payable in arrears, which are callable after 5 years at par. At the time of
issue, the market rate for this type of bond was 10% but one year later on 31 December 20x1
(after the coupon payment for 20x1), interest rates have fallen to 6% and this bond is now
trading at a market value of R110.
1. What would you expect the value of the bond to be on 31 December 20x1 (after the
coupon interest payment) if MTX was not permitted to redeem after 5 years?
2. What is the likely yield of these bonds at 31 December 20x1(after the coupon interest
payment) if we consider that the company is able to redeem (call) the bonds in 20x5?
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3. Assume the same information except that the bonds are not perpetual but are 10-year
bonds and are not callable. What would the Yield to Maturity be if the price of the bond
was trading at R110 on 31 December 20x1 (after the coupon interest payment)?
Solution
1. The value at 31 December 20x1 would be expected to be R166.67 (R10/0.06) as we are
effectively valuing a perpetuity.
2. It is likely that the company will call (redeem) the bond. The reason for the increase in
price, is due to the fall in interest rates and the company will be able to reissue bonds at
a lower interest rate at the end of 20x5 if interest rates are expected to remain low. The
yield to the call date and the yield an investor will earn is expected to be 7.04%.
3. If the investor pays R110 for the bond and the maturity date is in 9 years’ time, then the
yield to maturity will 8.37%.
In South Africa, Nedbank issued perpetual (non-callable) bonds at a floating (variable)
interest rate with the first tranche priced at 7% above JIBAR giving investors an initial rate of
14.367%. The Johannesburg Interbank Average Rate (JIBAR) is the interest rate that banks
lend and borrow from each other. At that kind of rate, why would you want your principal
back? However, the terms may indicate that these bonds are more like equity than bonds. We
will come back to bonds as sources of finance in Chapter 13.
SUMMARY
In this chapter, we have focused on an important and fundamental concept in financial
management, namely the fact that money has a time value. The time value of money is one
of the variables that affects the interest rate. Two other variables that affect the interest rate
are expected inflation and risk. The risk attached to an investment relates to the expected
stream of cash flows from the investment as well as the ultimate return of the capital sum
invested.
If money is being loaned or invested, the investor expects the future value to be greater,
because a reward for permitting another person the use of the funds must be received, in
addition to the repayment of the original amount invested. The future value is determined
by compounding the interest at the agreed rate. It may be important to calculate the
effective annual rate when comparing different options. This differs from the quoted rate
when interest is compounded more frequently than once a year. It is the effective rate which
is relevant for purposes of comparison and evaluation. Two basic types of future values can
be identified. They are the future value of a single amount investment and the future value
of an annuity.
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The determination of present values is even more important in financial management
than future values. Present values of cash flows will clearly be lower if the cash flows
are to be received in the distant future. The interest factor is therefore used to discount
expected future cash flows to their present value. Some present value calculations require
special attention. They are the cases of annuities due, deferred annuities, uneven streams,
perpetuities, and instalment loans.
Mortgage loan amortisations and retirement planning are two cases where time value of
money principles are applied. The valuation of bonds illustrates another significant area for
applying these principles. A bond is essentially a long-term loan, which offers the holder a series
of stable cash flows during its life and a repayment of the nominal amount on maturity date. It
was shown that the value of a bond may fluctuate dependent upon the coupon rate on the bond,
the yield to maturity required by investors and the period of time remaining to maturity.
We used examples to illustrate the more important formulae and to demonstrate the use
of the tables. We also expanded on the use of financial calculators and Excel Spreadsheets
to solve time value of money problems. The concepts developed are not complex. However,
great care must be taken to formulate each problem correctly and to recognise the type of
investment which a particular situation reflects. Many of the concepts developed in this
chapter will be used extensively later in the text.
S
SELF-STUDY PROBLEMS
S2.1
You deposit R10 000 in a bank account which is paying 4.8% per year, interest compounded
annually. How much will you have accumulated in the account in 5 years time? What will
you have accumulated if interest is compounded monthly?
S2.2
You have purchased a motor car for R120 000 and you have obtained a car loan for the total
amount, which requires you to pay this amount over 5 years at an interest rate of 7.2%. If
interest is compounded monthly, determine the monthly payment required over the 5 years
if the first payment is due immediately.
S2.3
What is the present value of a zero coupon bond, with a par value of R100, which is due to
be redeemed in 10 years’ time, when the current market interest rate for such bonds is 6%,
interest compounded semi-annually?
S2.4
You wish to purchase an apartment in Port Elizabeth which is situated in a tree-lined
avenue. The purchase price, with costs, is R710 000 and you are able to obtain a 100%
mortgage loan at an interest rate of 6%, interest compounded monthly. The term of the
loan is 20 years. Assume that property values are expected to rise at a rate of 9% per
year (0.75% per month). You will be able to rent out the apartment after costs at a rate
of R4 000 per month for the first year. Interest and rent are payable at the beginning of
each month.
Required:
What is the expected value of the apartment in 20 years’ time? What is the mortgage loan
repayment at the beginning of each month? What is the net amount you have to pay in each
month?
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S2.5
During 2017, Barcelona fans were in a state of anxiety. After the loss of Neymar to PSG, the
question on every fan’s lips was whether Lionel Messi would also be leaving as Manchester
City were waiting in the wings offering extraordinary sums of money and Messi had not signed
a new contract. Then the skies opened and in November 2017, it was announced that Messi
had signed a new contract to remain with Barcelona until 2022 (if we include a likely one-year
option). Messi is expected to receive €71m per year in wages (about R1.06 billion per year or
R21.1m per game). This is not all. According to Der Spiegel, there was a sign-on bonus payable
of €63.5m and a loyalty bonus of €70m. Assume that the sign-on bonus is payable on 30 June
2018 and the loyalty bonus is payable on 30 June 2021. There are performance bonuses as well
which we will assume to be about €2m per year. We will assume that these amounts are taxable
at a rate of 45% which is the current marginal tax rate in Spain. Income due to Messi from
endorsements are estimated to be €34m in the year ending 30 June 2018 but are expected to
grow at 10% per year until 2022.
Cristiano Ronaldo generates significant income from endorsement rights. For example,
the Portuguese footballer’s contract with Nike is worth $13m per year. Ronaldo also has an
incredible profile on social media with about 215 million followers across Facebook, Instagram
and Twitter and is estimated to create $176m in media value for his partners and sponsors from
his promotion of their products on social media. He also promotes his own products. We are
just going to focus on his income from wages and endorsements. Although Ronaldo had been
the highest earning footballer in the world up to mid-2017, this changed due to Neymar’s new
contract with PSG and Messi’s new contract with Barcelona. In July 2018 it was announced
that Ronaldo would be leaving Real Madrid and joining Juventus on a four-year contract for
a transfer fee of €100m (payable to Real Madrid). Ronaldo’s salary is €60m a year before tax
or €30m after tax as Italy’s tax rate is 50%. He will not receive incentive fees or performance
bonuses. Income from endorsements was estimated to be €40.3m for the year ending 30 June
2018 and is expected to increase by 10% per year until 2022.
Assume that the amounts due to Ronaldo are taxable at 50% and the amounts due to
Messi are taxable at a tax rate of 45%. Assume tax is due at the time of the payments and
that amounts are payable at the end of each year (apart from Messi’s bonus payments). Use a
discount rate of 4% per year.
Required:
What is the present value of Messi’s earnings in Euros? What is the present value of Ronaldo’s
earnings in Euros? Use an exchange rate of €1 = R14.88 to determine these amounts in South
African Rands (ZAR).
Solutions to Self-study Problems
S2.1
The future value at an interest rate of 4.8% with annual compounding is:
FV = 10 000 (1.048)5 = R12 641.73
The future value with monthly compounding is determined by using a monthly rate of 0.4%
(4.8%/12) and 60 months (5 × 12):
FV = 10 000 (1.004)60 = R12 706.41
The higher amount is due to interest earning on interest more often over the period.
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S2.2
This is an annuity due. The monthly payment on the car loan is determined by using
60 months and an interest rate of 0.6% (7.2%/12). Remember with an annuity due there is
one less discounting period.
{[
] }
1 – 
​  1 59 ​
(1.006)
​ ​+ 1 ​
120 000 = PMT × ​ ​ 
​
0.006
120 000 = PMT [50.5637]
PMT = 120 000/50.5637
PMT = R2 373.24 per month
If we use a financial calculator, then press 12 followed by SHIFT and P/YR to change the
financial calculator to monthly compounding. Also, press the SHIFT key and the BEG/END
key to change the mode to Beginning of the period, i.e. to indicate to the financial calculator
that the cash flows will occur at the beginning of each period.
The payment that is required to repay the loan and interest will amount to R2 373.24 per
month at the beginning of each month for 5 years.
S2.3
A zero coupon bond is a bond with no coupon payments and the value is dependent on the
redemption date and the par value. The par value is R100 and the redemption date is in 10
years’ time. The discount rate is 3% per half year and there are 20 six-monthly periods. The
value of the zero coupon bond is determined as follows:
PV = FV/(1.03)20
PV = 100/1.8061
PV = R55.37
S2.4
The expected value of the apartment in 20 years’ time is:
FV = 710 000 (1.0075)240
FV = 710 000 (6.009152)
FV = R4 266 498
If property keeps on appreciating at a rate of 9% per year, then the value in 20 years’ time
is expected to be over R4.2m. If the rate of appreciation is 6% per year then the value in 20
years’ time will be R2.35m, so 3% makes quite a difference.
The monthly repayment due at the beginning of each month is determined by applying
the annuity due formula:
710 000 = PMT ×
{[
] }
1
​
1 – 
​
(1.005)239
​  ​+ 1 ​
​ ​ 
​
0.005
710 000 = PMT/(140.2787)
PMT = 710 000/140.2787
PMT = R5 061.35
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You will need to pay in R1 061.35 each month after taking into account the net rental of
R4 000 per month. At a marginal tax rate of 40%, the interest and other costs would be
deductible for tax purposes. Remember that the rental should also grow over time.
Using a calculator and ensuring that you use a beginning of period mode and monthly
compounding as in S2.2 above, the payment is determined to be R5 061.35.
S2.5
The present value of Messi’s contract at 30 June 2018 is about €301m which equates to R4.48
billion. The cash flows are set out in the following spreadsheet. Income from endorsements
have been increased by 10% each year so that the earnings from endorsements for the year
ending 30 June 2019 is €37.4m (€34m  1.10). The sign-on bonus takes place on 30 June 2018
and the loyalty bonus is payable on 30 June 2021. We add the estimated performance bonus
and constant salary and then deduct tax at 45%.
The present value of Ronaldo’s future earnings and endorsements is €201.81m or R3.0 billion.
The income from endorsements is expected to grow at 10% per year, so that the expected
income in the year ending 30 June 2019 is €44.33m (€40.3m  1.10).
Note: We have used information from various news media reports to reach the estimates used in this question. We have
had to make a few assumptions as some media reports are inconsistent and Ronaldo’s contract had only been recently
announced at the time of writing (see Forbes 10 July 2018). Footballers may try and use corporate structures to reduce
tax payable on income from image rights or endorsements. Sometimes this results in challenges from tax authorities
on such structures which may use low tax jurisdictions. We have assumed that the income from endorsements and
image rights are taxed at the normal rate.
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APPENDIX 2.1: RETIREMENT PLANNING: LIVING ANNUITIES, THE 4% RULE AND
THE LOOMING PENSION CRISIS
I advise you to go on living solely to enrage those who are paying your annuities. It is the only pleasure
I have left. Voltaire. Money is something you got to make in case you don’t die. Max Asnas. You can
be young without money but you can’t be old without it. Tennessee Williams.
Time value of money principles are crucial in structuring retirement pensions and annuities.
We will expand on our example in the chapter by explaining the options facing South Africans
considering retirement. Persons approaching retirement will have contributed to a retirement
fund over their working lives and will then need to ensure that any accumulated sum generates
an adequate income to provide for them in their years of retirement. A retired person will have
two main alternatives, to either select a guaranteed life annuity or select a living annuity3.
A guaranteed life annuity is an insurance product whereby an insurance company will
guarantee a retiree a set annuity income for the life of the retiree. This may include an adjustment
for inflation, or fixed escalations and may offer other options. A person may have accumulated
within a retirement fund a total amount of say R3.0m. The retiree transfers this amount to
an insurance company who may promise, for example, to pay a pension annuity of R14 000
per month increasing by inflation each year for the life of the retiree. If the retiree dies after
2 years, then the capital normally dies with the retiree. However, the insurance company will
lose if the retiree lives for much longer than expected in terms of the actuarial life expectancy
tables. The advantage is that the pension annuity will last for life and is guaranteed (as long
as the insurance company remains in business). The insurance company will pool its longevity
risk across many annuitants. The quote above by Voltaire relates to a guaranteed life annuity.
However, a guaranteed life policy has the following disadvantages:
■■ Loss of liquidity and control over one’s assets. Once there is a transfer of the retirement
sum, a retiree can no longer recover the amount or have access to it. There may be
unexpected medical costs or other expenditure and there is no flexibility to access the
funds or pay for unexpected emergency expenditure.
■■ There is no legacy and a retiree will be unable to leave money to his or her heirs.
■■ High costs and lack of transparency.
■■ Insurance companies tend to focus on investing in fixed-income securities to support a
lifetime pension and this will normally offer lower returns (at a lower risk) than other
investment alternatives such as unit trusts which include ordinary equities. However,
insurance companies are starting to insert equity options and perhaps providing an
income component which is variable depending on the performance of the underlying
equity assets.
■■ Although unlikely, insurance companies sometimes fail. Annuities are paid over many
years and therefore the question of whether the company will be around in 25 years’ time
is relevant.
It may be possible to plan around these limitations by taking out an initial part of the retirement
sum as a tax-free amount and investing this outside the pension/annuity structure. Also, there is
greater flexibility these days with guaranteed life annuities and options may include a guaranteed
period or provide an annuity over the lives of both spouses. However, the impact of such options
on the promised annuity can be significant. The main benefit of a guaranteed annuity is that it
does provide protection against outliving one’s assets.
The alternative and significantly more popular retirement option in South Africa is a living
annuity. This is more aligned to an investment product but is subject to regulatory limits set
Almost all employees in the private sector will belong to a defined contribution retirement plan but
government employees will belong to a defined benefit plan. We explain the difference between these plans
later in this appendix. For now, we will only refer to members of defined contribution retirement plans.
3
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by government. A living annuity is offered by financial institutions and asset management
firms whereby a retired person will withdraw a regular income but this annuity amount is not
guaranteed as it depends on the lifespan of the retiree and the performance of the underlying
investments. This means that the retiree will bear the risks of longevity, investment returns and
inflation. In terms of the Income Tax Act which sets out the definition of a living annuity, a
retiree will be able withdraw between 2.5% and 17.5% of capital per year. For example, the
following is from Allan Gray’s Living Annuity terms and conditions (effective 9 March 2018,
version 12.2)
Your annuity income may differ from year to year. Neither the amount of the annuity income, nor the
return of the underlying investment, is guaranteed. The market value of the investment account may
fluctuate and you carry the risk of your capital and income being reduced.
A higher initial capital amount and a low drawdown per year will improve the chances that the
fund will provide a pension for life but for many pensioners the reality is that they may run out of
money during their lifetimes due to high drawdowns, low returns or living longer than expected.
A rough guide that has been often promoted is that the initial drawdown should be 4% for the
first year, and this initial amount can thereafter increase by inflation to retain its purchasing
power. A living annuity provides flexibility and if you die early, then there will be money to
leave to your family. Investment returns and capital gains in the fund are tax free but pension
payments are taxable. Let’s refer to an example and we will use annual amounts and include
inflation. We will ignore for now the regulatory constraints that the pension should be between
2.5% and 17.5% of the value of the investments in any year but we will come back to this later.
Let’s assume that Lerato Khumalo, a Chartered Accountant, is coming to the end of her
working life and has accumulated a sum in her defined contribution pension plan of R2.5m and
is looking forward to retirement. She needs a pension with a current value of R228 000 per year
to live on and this annual pension needs to increase at the expected inflation rate of 5.0% per
year. Assume the annuity is payable at the end of each year. She will invest in a diversified bond
and equity portfolio which is expected to generate a return of 10.0% per year4. She is 65 years
old and estimates that she will need a pension for 30 years. She owns her own home and there is
no mortgage loan, so if she lives longer than 30 years, then she will sell her home. Planning for
such a long retirement period means that she should be able to leave a legacy to her heirs as well.
If we apply Formula 2.13 for a growing annuity, we can determine that the capital amount
required to enable her to acquire an expected annuity with a current value of R228 000 per year
(or R239 400 at end of the first year) is:
[ 1 – (1.05) /(1.10) ]
30
30
PV = 228 000 (1.05) × ​ ______________
​
​  ​
0.10 – 0.05
PV = R3 602 088
This is important as it indicates that a sum of R2.5m is not sufficient to provide the necessary
income over her remaining life. It is important to know this upfront. If we redo the above
calculation with an annuity (with today’s value) of R158 241.56 per year increasing thereafter
by inflation so that the annuity at the end of the first year is R166 153.64, then the required
initial amount would be R2.5m. Is it possible for Lerato to obtain part-time work after
retirement to make up the annual difference between R166 153.64 and R239 400.00? Is it
possible to downsize and move into a smaller property and perhaps invest the difference to
ensure a total income of R239 400 per year from year one and which will grow by inflation
thereafter?
If we consider the long-term bond yield of 8% in early 2018, a market risk premium of 4% to 5% which
means that future equity returns should be about 12% per year, and an asset allocation of 50% equities and
50% bonds, then an annual return for the portfolio of about 10% seems reasonable in 2018. We will assume
that this return is after fees. Inflation should be around 5% in the longer term.
4
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Let’s now change our assumptions and we will now determine that Lerato has been able to
accumulate exactly R3 602 088 at retirement date. In this case, the value of her retirement assets
at the end of each year is set out in Figure 2.8. For example, at the end of years 1 and 2, the value
of the assets is equal to the beginning asset value multiplied by one plus the return of 10% less
the annuity for the first and second years:
R3 602 088 × 1.10 – R239 400 = R3 722 897
R3 722 897 × 1.10 – R251 370 = R3 843 816
What is interesting is that the value of Lerato’s investments will continue to grow until year
16 where it will reach R5 002 369m and even by year 24, the nominal value of her investments
at R3 760 860 will still be very close to what she began with, but will fall swiftly in value in
the last few years in order to fund the growing annuity. In the first 16 years, the return on the
investments will be higher than the inflation-adjusted annuity and this will increase the value
of the investments. However, from year 17, Lerato’s annuity will exceed the income from the
investments and she will begin to draw down capital. Therefore, there will be a growing capital
contribution each year to the annuity, due to lower income and a rising annuity payment, until
the value of the investments is zero at the end of year 30.
Figure 2.8 Value of retirement assets during retirement period
In Figure 2.9, we present the growing annuity, and the income per year as well as the capital
contribution. Until year 16, the capital contribution to the annuity is negative, which means that
we are accumulating capital (as income is greater than the annuity) but from year 17, we see
a growing capital drawdown to make up the required annuity amount. For example, in year 8,
investment income is R442 619, whilst the pension annuity is R336 860, which results in savings
of R105 759 which will increase the value of the retirement assets by the same amount.
In year 18, the annuity is R548 709 and income is R498 003, which means that the balance of
R50 707 is drawn from capital and the value of the investment assets will fall by the same amount.
In year 30, only R89 582 is from income and the balance of R895 821 (to make up the required
annuity of R985 403) is from capital, which will reduce the value of the retirement assets to zero.
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FINANCIAL MANAGEMENT
Figure 2.9 Living annuity with annual returns on retirement assets and capital contributions
If Lerato is able to accumulate R3 602 088 by retirement date, then she will have funded her
retirement perfectly. However, this is based on some perfect assumptions. If she dies early, then
any remaining balance in the fund will be left to her heirs, with the house. If she lives longer, then
this may create challenges for her, but she has a plan B which is to sell her house and move into
rented premises or enter into a reverse mortgage. Remember, she is planning for this upfront
so that it does not become an emotional issue for her later on. There are other options such as
renting out a room or renting out the house and moving into a smaller apartment at a lower
rental. These options should be explored a number of years before the 30th year of retirement.
There are other assumptions. The market has returned about 10% per year but this may not
apply in the future. If market returns are lower and the inflation rate is higher, then this may
place Lerato in a difficult position and so there should be some slack built in or Lerato should
try and save part of the annuity or perhaps reduce the required annuity in order to ensure that
there is a margin of safety. Currently, her home performs this role. We have assumed a return
of 10% after fees. What happens if the 10% return is before fees? A financial institution may
charge around 2% per year and this can have a material impact on the value of the retirement
assets over time. Only a few financial institutions or asset management firms are able to beat
the market index over time after costs. Investing in a low-cost market index may therefore be
a good alternative unless the manager can show outperformance over a sustained period of
time.
The 4% rule and the sustainability of a living annuity
A critical question facing any retiree is how much to withdraw from the fund each year. If a
retiree withdraws too much, then a retiree will run out of funds and may end his or her later
years in poverty. If the withdrawal rate is too low, then a retiree may experience hardship or
lower living standards during retirement. How much can a retiree safely withdraw each year in
real terms so that he or she does not run out of money? The annual withdrawals are affected by
equity and bond returns, asset allocation, inflation rates and the expected lifespan of a retiree.
William Bengen, a USA financial planner, decided to study historical equity returns, bond
returns and inflation rates over a long period for portfolios created each year since 1926 to
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test initial withdrawal rates over a retirement period of 30 years. The initial withdrawal amount
was then increased by the inflation rate each year to determine the annual withdrawal amount
for each year. The initial capital value was increased by the actual returns from a portfolio of
50% bonds and 50% equities, which was rebalanced each year, and the value of this portfolio
was reduced by the withdrawal amount each year. Bengen writes that “assuming a minimum
requirement of 30 years of portfolio longevity, a first-year withdrawal of 4%, followed by inflationadjusted withdrawals in subsequent years should be safe”5. This article led to the 4% rule that
financial planners tend to use around the world to determine a safe withdrawal rate. Later,
Bengen increased this rate to 4.5% but somehow the rate of 4% has become an institution in
financial planning circles. Bengen also indicated that a portfolio of 75% equities would improve
the longevity of a portfolio if investors were able to cope with a higher level of volatility. So, what
about South Africa?
Luckily for us, Michael Summerton, formerly of Allan Gray, did a similar study for South
Africa and considered equity returns, bond returns and inflation rates for South Africa6.
Summerton, in the Allan Gray study, went back to 1900 and created 84 30-year retirement
periods to take us up to 2014. Table 2.11 presents the results from Bengen’s study and from the
Allan Gray study.
Table 2.11 Withdrawal rates and the number of years a portfolio will last
The Allan Gray study supports Bengen’s original study and finds that portfolios subject to an
initial withdrawal rate of 4% would have lasted for at least 30 years, 93% of the time, and would
have provided a retirement income for at least 26 years, 98% of the time. The Allan Gray study
indicates that higher-than-inflation withdrawals would have had a significant negative impact on
the longevity of portfolios even at an initial withdrawal rate of 4%.
Withdrawals assuming a 5% initial withdrawal would mean a 7% risk that the portfolio would
last 20 years or less and a 21% chance that it would last between 21 and 25 years. This means
that, to be safe, retirees should select an initial withdrawal rate of 4% in South Africa. Another
study in the USA by Cooley, Hubbard and Walz7 supported a higher withdrawal rate of up to 6%
but this was based on returns from 1926 to 1995.
A more recent study by Morningstar8 which focused on Australia but also analysed
international returns for a number of countries, including South Africa, assumed a retirement
period of 30 years, a portfolio of 50% equities and 50% bonds and went further than other
studies by assuming an annual portfolio fee of 1% of assets.
The results for 99% and 95% success rates over 30-year retirement periods for the USA, the
UK, Australia (AUS) and South Africa (RSA) are depicted in Figure 2.10. For South Africa,
William P. Bengen. Determining withdrawal rates using historical data, Journal of Financial Planning,
171–180 [p173], October 1994.
6
Michael Summerton, “How to ensure your retirement income goes the distance”, Allan Gray Quarterly
Commentary, 2, 2014, 13–16.
7
Cooley, PL, Hubbard, CM and Walz, DT. “Retirement Savings: Choosing a withdrawal rate that is
sustainable”, AAII Journal, Feb. 1998.
8
Blanchett, D, Serhan, A, and Gee, P. “Safe withdrawal rates for Australian retirees”, Web: 2 February 2016,
https://www.morningstar.com.au/smsf/article/withdrawal-rates/7529?q=printme
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this study found that to achieve a 99% success rate, the initial withdrawal rate would need to be
about 3.2%.
Figure 2.10 Safe initial withdrawal rates at 99% and 95% success rates
The Allan Gray study indicated that a 4% rule would lead to a 93% success rate for a 30-year
retirement period but did not make an explicit adjustment for fees9 and assumed a greater
proportion of equities at 55% of the portfolio. Generally, these studies support the principle of a
low initial withdrawal rate to ensure that the real value of a pension annuity will be retained over
a retirement period of 30 years. This is not only true for South Africa, but for other countries
as well as set out in Figure 2.10. It is important to note again that increasing the proportion of
equities over lengthy retirement periods will tend to reduce the risk of outliving one’s assets and
running out of funds over the retirement period.
So where does this leave us? In our example for Lerato, we assumed a 10% portfolio return
which seemed reasonable in 2018. However, this implied a risk that the portfolio would not last
the full 30 years based on historical market returns and volatility as the withdrawal rate for year
1 was 6.65% of the opening value (R239 400/R3 602 088). If we wish to be safe that Lerato’s
portfolio will outlast her and we set the initial annuity at 4%, then the first-year annuity will
be R144 000 rather than R239 400, which is almost R100 000 lower. Alternatively, in order
to ensure that Lerato has an annuity of R239 400 in the first year, she would need to have
saved very close to R6m (R239 400/.04) in her retirement fund by retirement date. This indicates
the starkness of the choices facing people going into retirement. Assume Lerato started with
R3 602 088 and her initial withdrawal was R144 000. So, what happened?
Scenario 1: Lerato had a happy but very frugal retirement and died at 95 years old. The markets
provided the expected return of 10% and inflation was 5%. Lerato began with an initial 4%
withdrawal and did not increase her withdrawals above inflation. This resulted in significant
accumulation in her retirement waiting for a rainy day. When she passed away, she left a legacy
of R25m to her heirs.
Scenario 2: Lerato had a happy but very frugal retirement and died at 95 years old. The markets
experienced significant volatility and lower returns. Inflation was 5% per year and the portfolio
return was only 6% per year over 30 years. Lerato began with an initial 4% withdrawal and
It is important in our view to consider fees which may be in the order of around 1.0% to 2.5% for most
actively managed funds in South Africa. However, we need to consider this in line with the performance (and
risk) of each fund relative to the market benchmark. Therefore, if a fund manager can achieve a return that
matches the market benchmark after fees (VAT inclusive), then we think that it is more correct to assume a
higher withdrawal rate than indicated by Morningstar and therefore the 4% rule is probably more relevant. If
the performance of the fund is equal to the market index before fees, then it is relevant to include an estimate
for fees. The bottom line is to use an initial 4% withdrawal rate or lower and to increase the equity component
of the portfolio to ensure a safe financial passage over one’s retirement.
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did not increase her withdrawals above inflation. When she passed away, she left a legacy of
R218 000 to her heirs.
Limits on living annuities in terms of government regulations
In terms of government and SARS regulations, a living annuity withdrawal needs to be between
2.5% and 17.5% of the value of the retirement assets. We will ignore the 2.5% rule as this is
normally not a constraint for most people. As the pension annuity increases due to inflation
and the value of the investments and the annual return falls, then at some point the required
inflation-adjusted annuity will come into conflict with the regulatory limit that the pension should
not exceed 17.5% of the market value of the investments in any one year.
So, what is the effect of an underfunded pension plan in a regulated environment? What is
the real difference between a beginning amount of R2.5m at the start of retirement and R3.6m
if one wishes to earn a pension annuity of R228 000 in today’s money over the next 30 years?
What difference does a recommended withdrawal of 4% have in this case? The following reflects
a situation whereby a South African retires with R2.5m and draws down R239 400 from year 1,
which reflects an increase at an inflation rate of 5% per year. This reflects an initial withdrawal
of 9.58% of the opening value of R2.5m. For year 1, the inflation adjusted annuity is R239 400
(R228 000 × 1.05). Whilst the retiree is able to legally withdraw 9.58% initially, the effect is that
in real terms, after year 9, the actual annuity starts falling in order not to exceed the statutory
limit of 17.5% of the value of the investments. This results in a steady reduction in the nominal
and real value of the retiree’s annuity over time, leading to lower living standards and even
poverty. By year 20, the nominal value of the annuity should be R604 952 but the retiree will be
receiving only R163 134. The limit of 17.5% ensures that retirees maintain an annuity for life but
this falls dramatically over time. In year 15, the retiree is earning almost the same (R240 900) in
nominal terms as at the end of year 1 but significantly less in real terms. In this case the golden
years only lasted for 9 years. This situation is depicted in Figure 2.11.
Figure 2.11 Actual annuity subject to 17.5% limit and the required annuity to maintain lifestyle per year
The nominal value of the pension by year 30 should be R985 403 per year in order to retain the
purchasing power of R228 000 at the beginning of retirement. The effect of the 17.5% limit will
mean that the pension will last at least 30 years and there will be ending capital of R395 426 but
the pension annuity in year 30 will be R74 810, which is only 7.6% of the value that the pension
annuity should be in order to maintain the same standard of living as today.
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After 9 years, the pension annuity starts losing its real value and often pensioners are not ready
for these adjustments. It is critical to act early and take drastic action if required. Otherwise, if
you wait, it will be too late. It is important to plan from day one. To make the point more clearly,
is to ask the question whether it would be desirable or possible for a retiree to live on R17 328
per year today (7.6% of R228 000)? That is the future one will face if one does not engage right
away with the pension crisis which will probably occur in our lifetimes. You may consider that
this situation will only affect you in the distant future, but it may affect your parents or family
and it will therefore affect you.
Table 2.12 sets out the impact of reducing the withdrawal rate. Assuming the portfolio offers
an expected return of 10% per year (after fees) and inflation is 5%, then if the initial withdrawal
rate is 4% to 6%, the annuity will last in real terms for at least 30 years but will have varying
ending values. Whilst legislation permits a withdrawal of up to 17.5%, the reality is that investors
and retirees should understand the negative impact that a high withdrawal rate will have on the
future real value of their annuities.
Table 2.12 Withdrawal rates and the number of years a portfolio will last
In Table 2.12 we assumed that equity and bond markets will perform reasonably in the future
based on current bond yields and expected equity returns. However, let’s assume that the
portfolio return is 8% rather than 10% per year. This now means that an initial withdrawal of 5%
will offer a retiree a constant annuity in real terms for 26 years rather than 30 years. A withdrawal
rate of 6% will offer an annuity in real terms that lasts for only 19 years rather than 30 years. A
withdrawal rate of 7% will offer an annuity in real terms that lasts for only 14 years rather than
20 years. Only a withdrawal rate of 4% will ensure a constant annuity in real terms over 30 years
if the portfolio return is 8%.
We suggested actions that Lerato could take in our example such as downsizing and moving
into a smaller house and using the proceeds to invest to make up the difference in required
annuity income. Otherwise, a person considering retirement should try and work for longer or
take up part-time work or perhaps even rent out rooms and so on. Although these may be hard
choices for some people, it is easier than what is to come if action is not taken early to deal with
the pension crisis facing many people today.
We considered that it is important that the annuity increases by the inflation rate, but some
costs such as healthcare have been increasing at a higher rate than inflation. Whilst we did not
deal with asset allocation in any great depth, it is critical that retirees maintain at least a 50%
exposure to equities over the retirement period and accept market volatility. Investing in bonds
only, though less volatile, will have a negative impact over the long term on the value of the
portfolio.
What would happen if Lerato starts with a much larger fund balance of R3.6m on retirement
date, the portfolio provides a return of 10% per year and the inflation rate is 5% per year? In
Figure 2.12, we can see that, subject to the 17.5% limit, the pension annuity will continue to
provide a real level of income until year 23.
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Figure 2.12 Actual living annuity subject to 17.5% limit and the required annuity to maintain lifestyle per
year
It is only from year 24 that the pension annuity will fall in real terms as the annuity amount is
constrained by the 17.5% limit on pension payments. Therefore, the annuity in year 30, due
this regulation, will be close to 50% of the required annuity value and there will be capital of
about R2.36m at the end of year 30. The restriction of a 17.5% pay-out plays an important role
to ensure that a retiree does retain retirement funds if the retiree lives longer than 30 years
after retirement. However, this may come at the cost of a reduced annuity in real terms and
our determination indicates that even a R3.6m funded living annuity means an annuity in the
30th year that may be less than 50% of the required annuity if Lerato wishes to ensure that she
maintains the same standard of living as when she retired. If Lerato’s lifespan is 30 years after
retirement, and the life expectancy tables indicate an expected remaining life of about 22 years
for a woman at a retirement age of 65, then this means that there will be fund assets to leave
to her heirs plus her home. Although the limit of 17.5% does protect to some extent against
longevity risk, it may also impact on retirees such as Lerato and so it is important to evaluate a
person’s total financial position. There are ways to plan around this but this situation is not ideal
and indicates the complexity of effective financial planning in retirement.
On 12 November 2017, Laura Du Preez in Business Day titled her article as: SA retirees in living
annuity ‘crisis’: Thousands of elderly have had pensions halved in six years. The article reported that
more than 20% of all retirees drawing a living annuity were receiving half the income, adjusted
for inflation, as compared to six years previously. The Association for Savings and Investment
South Africa (ASISA) responded by indicating that the average withdrawal rate was 6.62%.
A National Treasury technical discussion paper, Enabling a better income in retirement,
published on 21 September 2012, states that charges on living annuities seem to be high at over
2%. The report states further that “a sustainable rate of drawdown for an individual aged 65 in
good health may be no higher than 5% per year”. The report indicates that there is a 2/3 chance
that an annuitant’s income will fall by 30% in real terms over an annuitant’s life.
These reports indicate that the challenges facing South African retirees are real and it is
important to keep to a withdrawal rate of 4% to 5%, in order to ensure that retirees do not
end up financially distressed in their later retirement years. Living annuities have distinct
advantages such as flexibility in relation to investments and the level of annuity income and
there is transparency in relation to returns, investments and fees. However, there are real risks
involved in relation to longevity, returns and inflation.
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Is there a pension crisis on the horizon?
There are two main pension systems; a defined contribution plan and a defined benefit plan. Most
companies in South Africa offer a defined contribution pension plan to their employees. In this
case, there will be an accumulated sum on retirement which is determined by the contributions
made to the fund by the employee and employer, plus the returns the fund is able to achieve on
these contributions over the period of employment. This accumulated sum may then be used to
acquire an annuity such as a living annuity or a guaranteed life annuity. The employee, and not
the employer, is subject to investment risks during the accumulation phase and investment and
longevity risks in the retirement phase, in the case of a living annuity.
In a defined benefit plan, the retirement fund will provide a pension to an employee based
on a formula which considers the length of employment and the final salary in determining
the annuity to be payable to an employee for life. In most cases, the employee and employer
contribute to the pension fund as a percentage of the employee’s salary over the period of
employment. The following would be an example of a defined benefit plan formula:
Pension annual annuity = Final salary × 2% × Number of years of service
If the final salary was R480 000 per year and an employee has been working at the firm for 25
years, then the final pension annuity would be R240 000 (R480 000 × 2% × 25). The trustees
of the fund may decide to increase the annual pension by inflation but there may be no legal
obligation to do so. In a defined benefit plan, the employee does not have to worry about
investment performance or longevity risk. The employer takes on these risks.
The Government Employees Pension Fund (GEPF), which is a defined benefit fund, manages
the pensions of all government employees in South Africa. It has more than 1.2 million active
members and provides pensions currently to over 400 000 pensioners and/or spouses. The GEPF
has over R1.6 trillion assets under management and is the largest pension fund in Africa and
one of the largest in the world. On retirement, a member will receive a once-off lump sum and
an annuity. The annual annuity is based on 1/55 of the final salary multiplied by the number of
years of pensionable service. The lump sum (gratuity) is 6.72% of the final salary multiplied by
the number of years of pensionable service. The annuity will last over the life of the employee
and thereafter 50% of the annuity will be paid to the employee’s spouse over her or his life. The
GEPF has been able to increase annuities in most years by inflation and is known to be a wellmanaged fund.
In most developed economies, the government will provide elderly people with an age pension.
Public entities such as state governments in the USA will provide pensions to employees such
as teachers and other public employees. In the USA and the UK, there are companies which
have defined benefit plans, although companies have been moving across to defined contribution
plans in order to reduce the investment and longevity risks implicit in defined benefit plans.
A World Economic Forum report in 2017 laid out the coming pension crisis facing developed
economies. The pension crisis arises from promises made to citizens and employees that are not
affordable nor sustainable. In terms of a Citi GPS report10 in 2016, it was estimated that the value
of unfunded or underfunded government pension liabilities for the 20 OECD countries was $78
trillion, which Citi reported was almost double the national debt of $44 trillion. It is expected
that a number of states or local counties in the USA may declare bankruptcy due to underfunded
pension liabilities. USA and UK companies providing defined benefit plans have had to make
increased contributions due to underfunded benefit plans.
Bloomberg reported in February 2018 that General Electric’s (GE) pension deficit alone was
over $31 billion. The challenges facing governments and companies providing defined benefit
plans relate to changing demographics and longevity as well as low interest rates. There is a
growing increase in the 65+ aged population and in the number of people living longer, which
The Coming Pensions Crisis: Recommendations for keeping the global pensions afloat, Citi GPS: Global
Perspectives & Solutions.
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results in greater pension obligations. Low interest rates and bond yields indicate that future
returns will be limited.
On 1 December 2017, PwC reported that the deficit of the UK’s 5800 defined benefit pension
funds was £450bn, with total pension obligations at £2010bn11. This is about 25% of the GDP of
the UK. It has been estimated that in the USA, underfunding of state pension schemes amounts
to about $1.4 trillion. Other estimates range from $1trillion to $3 trillion, depending on which
discount rate is employed.
How much companies need to contribute is a function of the expected rates of return on
the investments held in retirement funds. The average assumed rate of return used in actuarial
projections in 2017 for the top 100 USA companies in the S&P500 is 6.8%. The higher the
investment rate, the less the company needs to contribute in the future. Is this assumption fair?
If we assume that the investment portfolio will be 50% equities and 50% fixed-income securities
and the current bond yield is offering 3% in the USA, then equities will need to offer an annual
return of 10.6% over the longer term [50% × 3% + 50% × 10.6% = 6.8%]. Is this reasonable?
In the period 1900 to 2017, equities offered a real return of 6.5% and over the period 1968 to
2017, equities offered a return of 5.7% per year. If we add expected inflation in the USA of about
2%, it seems that an assumed return of 10.6% may be too high. This means that the reported
underfunding of the USA private sector’s defined benefit obligations may in fact be understated.
This is a rough estimate but points to a potential problem in expected returns and funding of
pension schemes. It may also indicate higher inflation in the future.
How does this affect South Africa? Firstly, most companies have shifted to defined
contribution plans and therefore are not at risk. The risk has shifted over to the employees as we
have set out in our example of a living annuity. Secondly, South Africa’s bonds are offering higher
long-term yields. If inflation adjustments are not obligatory, then this also provides protection
to a firm if there are falls in returns. Also, the GEPF has been adept at managing the pension
obligations of its members to date. However, if there are any significant bankruptcies in the USA
then this may lead to disruption in financial markets which will not only affect the USA but will
affect emerging markets like South Africa.
Although there may not be a pension crisis for the corporate sector in South Africa, our living
annuity example indicates that for many pensioners, a combination of high withdrawals, poor
investment decisions and living longer lives may lead to much lower living standards for retirees
in later years. The golden years may lose their lustre due to the foreboding clouds of financial
distress. It is important to act early – work longer, spend less, focus on your health, make your
assets work for you such as your property, adhere to a low withdrawal rate in the early years
of about 4% if possible, minimise fees unless there is outperformance after fees, and remain
invested in equities even over periods of volatility. Acquire knowledge about investments, risk,
investment managers and about how pensions and annuities work. It is important to know what
is on the investment horizon in order to plan effectively for retirement. We prepare for storms
by trimming our sails in order to ensure a safe passage.
https://www.pwc.co.uk/press-room/press-releases/uk-pension-deficit-climbs-40bn-in-November-accordingto-pwc-skyval-index.html
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Q
QUESTIONS
Question 2.1
How much will you accumulate if you are offered the following investments?
■■ R10 000 invested for 12 years at an interest rate of 8%, interest compounded annually.
■■ R12 000 invested for 6 years at an interest rate of 6%, interest compounded annually.
Question 2.2
How many years will it take for R1 000 to become R2 000 if an investment offers 6% per year,
interest compounded annually?
Question 2.3
To what amount will regular payments of R1 500 per month at the start of each month accumulate
by the end of two years if the payments are earning interest monthly at 6% per annum?
Question 2.4
You wish to travel to Europe in 5 years’ time and you will need R30 000 at the time. If you currently
have R15 000, what interest rate must you earn each year to reach R30 000?
Question 2.5
A bank is offering 6% per year, interest compounded monthly on a Special Savings account. If
you deposit R8 000 today, how much will you accumulate by the end of 10 years? What is the
annual effective rate?
Question 2.6
Calculate the future value of a R2 000 investment made now under each of the following interest
rate and investment period alternatives. Assume annual compounding.
Question 2.7
Use the investment alternatives in Question 2.6 but assume that semi-annual compounding is
available on your initial investment. What will be the future value for each investment alternative?
Also calculate the future values assuming quarterly compounding.
Question 2.8
A student borrowed R5 600 at the beginning of each year at 8% p.a. compound interest. How
much is owed at the end of her third year?
Question 2.9
You are planning to take a holiday in Mauritius when your current savings of R10 000 reach R20 000.
(a) If you plan to take your holiday at the end of five years from now, what annual rate of interest
will you have to earn on your savings account?
(b) If you are willing to wait seven years before taking your holiday, what annual rate of interest
would be necessary on your savings account?
(c) If you can earn 7% per year compounded semi-annually on your savings account, how long
will it take before you have adequate funds to take your holiday?
Question 2.10
If a lump sum of R8 000 left in the bank for four years has grown to R10 164 with interest
compounding and paid at the end of each month, what annual rate of interest has the bank been
paying?
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Question 2.11
The manufactured price of an article was R2 880. Every time the article changed hands, the price
was raised by 20%. If it was eventually sold for R5 972, how many times did it change hands?
Question 2.12
In terms of a bequest, a man can receive R2 250 immediately or R3 600 in 12 years’ time. At what
rate is compound interest earned, on an annual basis?
Question 2.13
At the birth of his daughter, a man invested R1 000 at 6% p.a. compounded annually. What
amount would accrue to her if she left the money invested until she attained the age of
(a) 18 years, (b) 21 years, (c) 40 years, (d) 60 years?
Question 2.14
A special savings bond pays R30 in 10 years for each R10 invested today. At the time of his son’s
birth a man invests R5 000 in such bonds and at the end of 10 years reinvests the maturity value
of the bonds at 12% p.a. compounded half-yearly. How much will be available to his son at age
18? Would it have been better for the father to have invested the original R5 000 immediately in
the 12% investment?
Question 2.15
A bank agrees to lend you R10 000 today in return for your promise to pay the bank R18 380 in
nine years’ time. What rate of interest is the bank charging you?
Question 2.16
An individual has just put her life’s savings into a bank account yielding 4% p.a., interest
compounded semi-annually. Assuming she makes no withdrawals, how long must she wait until
she has doubled her money?
Question 2.17
Mr A. Miller is a young financial director of a listed company. Although he enjoys his work, he
wants to retire at the age of 35 (in 10 years’ time) and go sailing in the Mediterranean around the
Greek islands. He estimates that he will need to have R1.2m to buy the yacht and an additional
R200 000 to pay for supplies and mooring costs. Mr Miller intends to make equal annual payments
into a bank account on which he can earn 6% interest compounded annually.
(a) What amount must Mr Miller pay annually to achieve his objective in 10 years’ time? The
first payment is to be made at the end of the first year.
(b) Instead of making equal annual payments, Mr Miller wants to make one single sum payment
today, investing it at 6% interest compounded annually. What should this single sum be?
Question 2.18
You borrow from Better Bank to buy a car, and make monthly repayments of R1 053.35 at 12%
p.a. compounded monthly. Your loan is for a period of 4 years. How much did you borrow?
Question 2.19
You want to travel to Brazil to visit friends when you graduate three years from now. The trip is
expected to cost a total of R20 000 at that time. You have deposited R12 000 in an account paying
6% interest annually, maturing three years from now. You have inherited a further lump sum and
plan to use it to finance the balance. If you are going to put this money in an investment earning
10% per year over the next three years, how much must you deposit now, so you can visit your
friends at the end of three years?
Question 2.20
You can buy a music system for one cash payment today of R6 600 or ten quarterly payments
of R750, starting at the end of three months. If you could invest the cash and earn 6% per
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annum, with quarterly compounding, would you prefer to pay in cash or make the quarterly
payments?
Question 2.21
You have just received an inheritance of R329 760. You plan to put the entire amount in an
account earning 8% compounded annually and to withdraw R40 000 at the end of each year. For
how many years can you continue to make the withdrawals?
Question 2.22
You buy a studio apartment for R800 000 and put down a deposit of R200 000. Your repayments are
R6 673.35 per month for the 15 years you intend to pay the apartment off in. What is the annual
rate of interest on this loan?
Question 2.23
If your company borrows R2 000 000, repayable over ten years at 9% per annum with annual
compounding and equal annual payments, how much of the loan will be outstanding after three
years?
Question 2.24
A retirement plan guarantees to pay you or your estate a fixed annual amount for 20 years. At the
time of retirement you will have R313 600 to your credit in the plan. The plan anticipates earning
10% interest annually over the period you receive benefits. How much will your annual benefits
be assuming the first payment occurs 1 year from your retirement date?
Question 2.25
WEC Ltd is planning to save R2 million per year for five years. The first deposit, which is presently
being made, and all subsequent deposits, will earn interest at a 12% annual rate.
(a) Calculate the future value for this annuity if interest is compounded semi-annually.
(b) Calculate the future value for this annuity if interest is compounded quarterly.
(c) How would your answer in part (a) have changed if the initial deposit was not made until the
end of the first year?
Question 2.26
A student managed to acquire an interest-free loan of R80 000. After completing her studies and
beginning to work, she saves R15 000 every year and invests the amount at 12.5% p.a. compound
interest. What additional amount is required to fully repay the loan after four years of saving?
Question 2.27
In order to provide for R10 million to build a new warehouse in five years’ time, a company
plans to make equal payments at the end of each six months into a fund which earns 9% per
year interest compounded semi-annually. After two years of payments, escalating costs lead the
directors to increase the semi-annual deposit so that the fund will contain R12 million at the
scheduled time of building. Find the increased semi-annual payment required for the remaining
3 years.
Question 2.28
A company has taken out a R480 000 loan. The loan is due at the end of six years, and the
repayment amount is R779 648. What is the interest rate that the company is charged?
Question 2.29
A man wants to have R48 000 in eight years’ time, so he decides to invest a certain sum half yearly
at 14% p.a. interest compounded semi-annually. He invests the first sum at the end of the first six
months and the same sum every half year thereafter. What would the difference in the instalment
have been if he had paid the first instalment immediately?
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Question 2.30
If a company wants to accumulate a total amount of R500 000 in 20 years’ time, what annuity amount
must it invest at the end of each year during the 20-year period? The applicable interest rate is 10% p.a.
Question 2.31
If you purchase an asset for R520.60 and it yields R100 per year for seven years, what is your rate
of return on this investment?
Question 2.32
Assume a 13% RSA Government security (par value R100) with a redemption date of 15 July
2033, was quoting a yield to maturity of 8% on 16 July 2015. RSA Government Securities pay
interest semi-annually. Determine the market price of the 13% RSA security on 16 July 2015.
Question 2.33
A loan of R1.5 million was made to a farmer, bonded against fixed property at an interest rate
of 8% p.a. compounded quarterly. The farmer agreed to pay off the loan in equal quarterly
instalments over a period of 12 years. As a result of severe drought, at the end of five years, the
farmer requested relief. It was agreed that the interest rate would be reduced to 4% p.a. By how
much will the quarterly repayments of the farmer be reduced?
Question 2.34
Longlife Insurance Company agrees to buy the entire R100 million issue of 14% debentures of the
Expand Manufacturing corporation, provided that the price will allow a yield of 8% per year compounded
semi-annually. The debentures carry semi-annual interest and are redeemable at par in 20 years. How
much cash does the corporation realise from the sale, if brokerage is 1% of the sale price?
Question 2.35
Calculate the annuity, payable in 12 annual instalments, which can be bought for R5 000 cash if
the first instalment is paid immediately, and interest is compounded at 11% p.a.
Question 2.36
On his son’s 12th birthday a father wants to invest a certain amount to enable him to withdraw
R8 000 each quarter from his 17th to his 21st birthday. Calculate the sum he will have to invest if
compounded interest is reckoned at 12% per annum, compounded quarterly.
Question 2.37
CC Company Ltd wants to establish a series of uniform deposits to be made on 1 January of 2x04,
2x05, 2x06 and 2x07 into a fund in order to make withdrawals of R2 million on 1 January 2x12,
2x13 and 2x14. What must the size of these deposits be to enable CC to make withdrawals if the
fund will earn interest at the rate of 12% p.a. interest compounded annually?
Question 2.38
What is the present value today of a perpetuity that pays R400 per year if the first payment does
not begin until four years hence and if 10% is the relevant discount rate?
Question 2.39
A machine is bought with a loan which must be repaid in 20 equal half-yearly instalments of
R6 500. The first instalment is payable four years after the loan has been negotiated. What is the
price of the machine if compound interest is added every half year at 14% p.a. on the outstanding
amount?
Question 2.40
A firm’s earnings per share grew from R5.78 to R12.48. During the same ten-year period, its
sales grew from R60 million to R156 million. Calculate the difference in growth rates between
EPS and sales.
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FINANCIAL MANAGEMENT
Question 2.41
A non-redeemable preference share pays a R15 dividend each quarter. What is the maximum
price an investor should pay for the share if a yield of 8% per year is required?
Question 2.42
Normal carpeting costs a company R280 per running metre and lasts five years. Is it more
economical to purchase a special fibred carpet at R420 per running metre which will last eight
years if the money is worth 12% p.a.?
Question 2.43
What is the value of an investment at the end of 20x9 if you intend to contribute R10 000 at the
beginning of each year from 20x5 to 20x9? You can earn an interest rate of 6% p.a. (interest
compounded monthly).
Question 2.44
You want to retire in 30 years and will require a monthly income of R20 000 for 10 years after
retirement date. If the return you can obtain is 12% p.a. (interest compounded monthly), how
much must you contribute every month for the next 30 years in order to obtain an annuity of
R20 000 per month for 10 years after retirement date?
Question 2.45
You bought a small apartment for R950 000 on 1 February 20x4 (registration date) and you
obtained an 80% mortgage bond on that date. The bond interest rate since 20x4 has stayed
constant at 7.2% per annum, interest compounded monthly. The rate of 7.2% is the actual return
that the bank is earning. Bond repayments are payable in advance on the first day of the month.
The mortgage bond had a term of 20 years from 1 February 20x4. What is the capital balance
outstanding on your bond on 1 April, 20x13 (before April’s bond repayment)?
Question 2.46
You have started a small manufacturing company. You have bought a machine in terms of a
suspensive sales agreement whereby you are required to make equal monthly instalments from
today, 1 April 2x08, to 1 March 2x13. The cash price of the machine is R220 000. Finance charges
are linked to the prime overdraft rate. The bank will charge you a premium of 1% above the
prime rate which is currently 11%.
Required:
(a) Determine the equal monthly instalment amount required to purchase the machine over five
years.
(b) If the prime rate increases to 14% today, before your first instalment payment, what will be
the increase in your monthly instalment amount?
(c) The bank offers to give you a three-month “holiday” so that you acquire the machine today
but the monthly repayments begin on 1 July 2x08. The last payment is still on 1 March 2x13.
What will your monthly instalment be if the prime rate is currently 11%?
Question 2.47
SX Company has issued 3 353 793 cumulative redeemable preference shares. The following is an
extract from SX’s annual financial statements for the year ending 30 June 2x04.
The cumulative redeemable preference shares carry a dividend of 12.5% per annum on the issue price
of R1.00 per share and will be redeemed at a price of R1.00 per share in five equal annual instalments,
payable on 31 December each year, commencing on 31 December 2x05.
Assume the preference dividend is payable annually on 31 December. Investors require a
return of 9% p.a. (interest compounded annually) on similar preference shares.
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2-59
Required:
Determine the price you would be prepared to pay for 100 SX Ltd cumulative preference shares.
Assume the current date is 31 December 2x04 (ex. dividend). Your share will be redeemed in five
equal annual instalments.
Question 2.48
You have purchased a pre-owned motor vehicle in terms of a suspensive sales agreement. You are
required to pay monthly instalments from today, 1 June, 2x01 to 1 May 2x06. The cash price of the
car is R128 496.00. Finance charges are linked to the prime overdraft rate; the rate is prime plus a
premium of 1% per annum. The prime rate is currently 8% per annum, interest compounded monthly.
Required:
(a) Determine the equal monthly instalment amount required to purchase the motor vehicle
over five years.
(b) If in a year’s time, on 31 May 2x02, the prime rate increases to 11%, what will be the new
monthly instalment amount from that date?
Question 2.49
Mirton Ltd has non-cumulative, non-redeemable preference shares in issue. The issue price was
R1.00 each and the coupon preference dividend rate is 12% per annum, payable once a year in
arrears. The company has not paid out a dividend in recent years but expects to recommence
dividend payments in two years’ time from today. What is the value of each preference share if
similar preference shares are quoting yields of 9% per annum?
Question 2.50
Mr Smart has just turned 50 years old and wishes to plan for his retirement at the age of 60 in
10 years’ time. He is considering either investing R90 000 at the end of each year over this 10year period in a mutual fund or investing R150 000 per annum in an all-equity retirement fund.
Mr Smart is on a marginal tax rate of 40% and his annual contribution to the retirement fund
will be fully tax deductible. You may assume that any tax benefit will be realised at the same time
as the contribution during the initial 10-year period. His annual contribution to the mutual fund
is not tax deductible. In 10 years’ time, the total accumulated amount in the mutual fund may be
withdrawn and is subject to tax at a rate of 10% of the difference between cost and the selling
price. If Mr Smart selects the retirement fund option then the accumulated amount must be used
to acquire a 10-year annuity which is taxable.
When Mr Smart retires, he expects his marginal tax rate to decrease to 30%. The financial
institution expects both the retirement fund and the mutual fund to grow at an annual
compounded rate of 9% over the initial period. The financial institution will be able to acquire
a monthly annuity on Mr Smart’s retirement, which will result in a return of 9% per annum,
interest compounded monthly. This reflects Mr Smart’s required return on funds invested
during his retirement period. You may assume that tax is payable once a year, at the end of each
year. You may assume that differences in transaction costs for the two options are immaterial.
Mr Smart is in a position that he will not pay tax on any mutual fund income. The mutual fund
income is immediately reinvested, and forms part of the 9% annual return.
Required:
Determine whether Mr Smart should select the retirement fund option or the mutual fund option
based on the value relative to cost of each alternative on retirement date if he wishes to maximise
his after tax wealth.
Question 2.51
You are considering investing in a fund whereby you will receive one third of the accumulated
sum as a single sum payment in 30 years’ time on retirement date, and a monthly income of
R24 000 for 10 years subsequent to retirement date. You will undertake the policy through one
of the major financial institutions which can earn a return of 6% per annum, interest compounded
monthly.
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FINANCIAL MANAGEMENT
Required:
Determine the monthly contribution that you are required to make over the next 30 years to
obtain the single sum payment on retirement date and a monthly income of R24 000 for 10 years.
Question 2.52
Two years ago, A Ltd needed to accumulate a total of R600 000 by the end of four years to acquire
new imported plant and machinery from an Italian supplier. To do so, A Ltd makes equal semi-annual
deposits into a fund which earns 8% per annum, interest compounded semi-annually. To date, the
company has made four equal semi-annual deposits into the fund. The rand has recently declined
against the Euro, and to acquire the plant and machinery, A Ltd now requires to accumulate a total
of R1 000 000 in two years’ time. However, A Ltd can from now on earn 10% per annum, interest
compounded semi-annually. All monies accumulated to date will from now on earn a return of 10%
per annum, interest compounded semi-annually. What is the increased equal semi-annual deposit
that A Ltd will need to make so that the fund will contain R1 000 000 in two years’ time?
Question 2.53
A 6-year bond, an RSA Government Security with a nominal value of R100 000 and coupon rate
of 9% is issued today, when the YTM required by investors is 9%.
Required:
(a) Calculate the present value of the stream of coupon payments, excluding the nominal face
value payable on maturity.
(b) Calculate the present value of the nominal face value of the bond.
(c) Sum the two values obtained in (a) and (b) above, and briefly explain the reasons for the
amount that you have calculated.
(d) Without further calculation, estimate what the value of the bond will be in three years’ time,
if the YTM remains unchanged, and explain your choice of estimate.
Question 2.54
A 20-year RSA Government Security with a nominal value of R10 000 and coupon rate of 6%
was issued 15 years ago, when the YTM required by investors was 6%.
Required:
(a) Calculate the value of the bond 12 years ago, when the YTM was 6%.
(b) Calculate the value of the bond today, if the required YTM is 12%.
(c) If the YTM changed to 10% today, as a result of a decrease in interest rates in the economy,
calculate the value of the bond today using a YTM of 10%.
Question 2.55
As a bond portfolio manager, you purchase a 10% RSA Government Security with a nominal
value of R10 million. It has 7 years to maturity. The yield to maturity (YTM) at the date of
purchase is 12%, which is immediately after the coupon has been paid. You hold the bond for
exactly 1 year, receiving the next coupon, and then sell the bond. The YTM at the date of sale
has fallen to 9%.
Required:
(a) Calculate the amount received from the coupon payment.
(b) Calculate the price that you paid for the bond.
(c) Calculate the price for which you sold the bond.
(d) Explain the reason for the profit or loss which was made over the one year holding period,
with reference to the principles underlying the time value of money.
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RISK AND RETURN
3
THE 21ST CENTURY: A TIME OF FINANCIAL CRISIS AND RECOVERY FOR EQUITIES
The financial crisis, market turmoil and falling equity values reminded investors that investing
in equities often involves taking on significant levels of risk. Although equity markets have
recovered, we should not forget how large the falls in equity values were in late 2008 and early
2009. Let’s place the financial crisis in context. Credit Suisse reported that the developed World
Index fell by 55% which represented a loss of R150 trillion or R150 000 for every man, woman
and child in the developed world1.This is serious, but we should also consider equity returns
over the longer term and that additional risks should be rewarded with higher returns. The
developed world index for the ten years to 2010 offered investors a return that was close to zero.
It began with the crash of technology and telecommunication equity values in the USA when the
NASDAQ index lost about 80% of its value.
By the time of the Iraq war in 2003, world equities fell again but recovered strongly until the
global financial crisis in 2008 and early 2009. Yet emerging markets performed strongly and
offered very positive returns for investors up to 2011. South Africa is an emerging market and
experienced positive gains in equity values from 2001 to 2013. The question is whether the higher
returns in emerging markets came with higher risks.
In 2013, 2014 and 2015, emerging markets experienced a significant amount of volatility and
capital outflows which were matched with falls in currency values. In the USA, equity values
increased significantly from 2010 due to very low interest rates, quantitative easing (the printing
of money), and economic recovery matched with significant corporate tax cuts. The S&P500
raced ahead from about 1 100 in January 2010 to 2 782 in June 2018. Market volatility was
low – perhaps too low. The question in 2018 is whether volatility will return and whether equity
markets will fall or stabilise? Emerging markets had a stellar year in 2017 but in 2018 there
were significant devaluations of emerging market currencies. Yet, USA equity markets and other
developed markets continued to race ahead. Is overconfidence in the bull market going to lead
to a fall in equity values? Low volatility and rising equity values may lead investors to take on
greater risks until we reach a Minsky moment when “stability begets instability”2. Is it possible
that behavioural finance can explain market movements and may it guide us to be calm when
others are diving into pools of “irrational exuberance” or despair?
In this chapter, we firstly analyse risk in terms of operating and financial leverage. The chapter
explains expected returns, the normal distribution and measures of volatility such as standard
deviation. The chapter concludes with the analysis of risk and return in financial markets.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Distinguish between business risk and financial risk.
■■ Calculate indicators of returns based on earnings before interest and tax (EBIT),
percentage return to shareholders, expected return based on probabilities, arithmetic
average returns, compound annual returns and total shareholder returns.
■■ Explain and calculate indicators of risk such as degree of operating leverage, degree
of financial leverage, variance of returns, standard deviation of returns, co-efficient of
variation, the z score, covariance and correlation, and Value at Risk (VaR).
■■ Understand the history of equity returns and bond returns.
■■ Define risk-adjusted measures of performance.
■■ Explain the behavioural finance view of risk and return.
Credit Suisse Global Investment Returns Yearbook, 2009.
Minsky was a US economist who studied how excessive borrowings and prosperity can lead to financial
instability and a Minsky moment refers to a sudden sharp decline in markets after a period of economic prosperity,
excessive borrowings, low volatility and high asset valuations.
1
2
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FINANCIAL MANAGEMENT
INTRODUCTION
Financial management is about making investment and financing decisions. Such decisions involve
risk. What is risk? How do we determine required returns? It is understandable that an investment’s
risk will affect the required return. The higher the risk, the higher the required return. So, what kinds
of risks do companies face? When a company builds a new manufacturing plant, there is the risk
that the product will not sell sufficient units for the company to break-even. Further, the company
may not be able to achieve the expected price due to unexpected competitive pricing decisions.
A high level of operating leverage may mean that a company’s earnings are significantly affected
by a small change in sales. A mining company such as Gold Fields may find that the initial capital
cost and the ongoing costs of operating a gold mine may be significantly higher than expected
at the time of the investment. A company borrowing funds may be subject to interest rate hikes
which may result in reduced cash flows. Yet, companies may experience substantial improvements
in operating returns due to unexpected price increases. For example, South32’s investment in
the Mozal smelter was undertaken when the price of aluminium was about $1 100 per ton. In
2006, the price was over $2 700 per ton. In 2008 the aluminium price fell dramatically from over
$3 000 per ton to about $1 200 during the economic crisis. After recovering to reach about
$2 000 in 2014, the price then collapsed in 2015 to under $1 500. However, by June 2018
the price of aluminium had recovered to $2 300 per ton. Aluminium is a major component
of numerous products and this price volatility creates risks for manufacturers. Risk is often
measured in terms of the volatility of expected returns and the potential for loss. In order to
make investment decisions we need to measure and adjust for risk.
Few questions about future events can be answered with certainty, because we don’t know
whether these decisions are good or bad until future events either confirm or repudiate the
expectations on which the decisions were based. Money is invested by financial managers in
assets which, it is forecast, will generate income and increase the value of the firm. Similarly,
investors make investment decisions based on their expectations, and only in the future
will it be possible to determine whether these investments were profitable. Evidently, not
every investment decision will be profitable, because no one can consistently make accurate
predictions about the future.
Making predictions is clearly hazardous because you will sometimes be wrong. Methods
must be sought to keep the margin of error as low as possible. Information about the past
must rank as a significant input into predictions about the future. However, if it is known
that the past is unlikely to be replicated in the future, information about past events is of
little value and must be replaced with realistic estimates of future expectations. This chapter
suggests methods by which expected return can be measured. It discusses the uncertainty
that surrounds such expected returns – i.e. the risk that the returns may not be achieved –
and measures this risk. This requires the application of certain basic statistical techniques.
Once we determine how to measure an investment’s expected return and its associated
risk, we compare investments with different risk and return profiles. We thereby lay the
foundation for the study of portfolio theory in Chapter 4.
The historical evidence of share returns will be examined in the last section of this
chapter. We evaluate the international and South African evidence of whether the higher
risk of investing in equities was rewarded with higher returns. Did equities offer returns that
were higher than bonds?
Investment risk can be measured by comparing the risk of one investment with that of
the market as a whole. This risk comparison is denoted by a firm’s beta which measures the
relative volatility of a share to the market. If a firm’s beta is 1.2, then this means that the
firm’s shares are more volatile than the market. If the market goes up by 5%, then we would
expect the share price of the firm to go up by 6% (5% 3 1.2). The market is assigned a beta
score of 1.0 and every share has a score that can be measured against this norm. We write
about this measure of risk in Chapter 4.
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3-3
1 THE CONCEPT OF RISK
The word risk is usually used in the context of a potential hazard or the possibility of loss
resulting from a given action. In financial management, the term indicates that there is an
expectation that the actual outcome of a project may differ from the expected outcome. The
magnitude of the possible difference reflects the magnitude of the risk. Risk may also be
positive as you may receive more than you expected from your investment.
The terms risk and uncertainty are often used interchangeably. There is, however, a
formal difference between these two terms. Uncertainty implies either that all the alternative
possible outcomes cannot be identified or that no probability can be attached to the alternative
possible outcomes. Risk implies that it is possible to attach probabilities to identified expected
outcomes. This strict distinction between the two terms is, however, not necessary for our
purposes.
From the viewpoint of an investor, investment opportunities can be broadly classified
into two categories:
■■ Investment opportunities with certain outcomes (no expectation that the actual outcome
will differ from the expected outcome); and
■■ Investment opportunities with uncertain outcomes (some probability that the actual
outcome will differ from the expected outcome).
An example of a certain outcome is an investment in 8% government bonds, maturing
in ten years. This may be regarded by some to have a measure of uncertainty should the
government not honour its obligation, but insolvency of the country implies that all other
investments are at least as badly affected. The South African government, with its power to
manage the money supply and to impose taxes, is accepted to be the ultimate benchmark of
risklessness in the economy. Examples of investments with risky outcomes are the purchase
of shares on the JSE or the purchase of fixed property with a view to deriving capital gains.
A pertinent question is: why would an investor prefer a risky investment to one that is
risk-free? The answer is that it offers a higher expected return. However, this does not fully
answer the question why some investors prefer risky investments while others avoid risk.
The preference for risk which some investors exhibit is generally accepted to be a function
of the utility which an individual derives from making the investment. Because individuals
differ both in their needs and in their personality traits, it follows that there will always be
a spectrum of investors, some of whom are more prone to looking for high-risk investments
with high expected returns, while others will maximise their utility through accepting lower
expected returns with concomitant lower risk.
Risk is also a function of age. Older investors approaching retirement do not readily
embrace risk as they do not have the ability to replace investment losses whereas the young
are more prone to embrace risk. This is why financial planners need to consider the age and
thus the risk profile of their clients when compiling appropriate investment portfolios.
Turning specifically to investment in the shares of listed companies, there are two major
areas of risk which will be considered by potential shareholders: business risk and financial risk.
Business risk
Business risk results from the nature of the business itself. It includes all the uncertainty
that surrounds the industry in which the business operates. This is reflected in the variability
of sales and the structure of costs. The variability of sales results from factors such as the
likelihood of increased competition, the availability of substitute products, and the effect
of recession. Rapid changes in technology and market shifts are also factors that may lead
to increased business risk. The structure of costs depends on the relationship between
fixed and variable costs, illustrated in Example 3.1. The effect of business risk on financial
performance is measured by the variability of earnings before interest and taxes (EBIT).
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FINANCIAL MANAGEMENT
Example 3.1: Cost–volume–profit analysis
Leverage Ltd has the following budgeted information:
■■ Fixed costs (F) R10 million per year;
■■ Variable costs (VC) R400 per unit;
■■ Selling price (S) R1 000 per unit; and
■■ Expected demand 30 000 units (minimum).
Figure 3.1 illustrates these facts graphically. It is apparent that sales revenue increases in
proportion to demand. Fixed costs remain constant within a relevant range regardless of
the sales volume, while variable costs commence at zero and increase in proportion to units
sold.
Figure 3.1 Behaviour of costs and revenues
In order to match sales revenue against total cost of sales, fixed costs (such as rent, depreciation,
and administrative overheads) and variable costs (such as materials and direct labour) must
be added together. The point at which sales revenue equals total cost is the volume of sales
required in order to break even, that is, to make neither a profit nor a loss. This is illustrated in
Figure 3.2.
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3-5
Figure 3.2 Break-even volume
It is apparent from the graph that around 16 600 units must be sold in order to break even.
If demand falls below 16 600, a loss will be incurred. Note that each time a unit is sold, it
makes a contribution of R600 toward the fixed cost (R1 000 – R400). No profit is earned
until all fixed costs have been covered. The break-even point, that is, to make neither a
profit nor a loss, can be precisely calculated using a simple formula, as follows:
fixed costs
(Formula 3.1)
Break-even units =
contribution
per
unit
=
=
F
S – VC
10 000 000
1 000 – 400
= 16 667 units
Once the break-even number of units has been sold, each additional unit sold will add its contribution
(R1 000 – R400) to the profit. Table 3.1 indicates the effect on EBIT of different sales volumes.
Table 3.1 Effect of volume on EBIT of Leverage Ltd.
It can be seen that, while sales increase by 33​ _13 ​% from 30 000 units to 40 000 units, EBIT has
increased by 75% from R8m to R14m. This results from the leverage effects of fixed costs.
The degree of operating leverage obtained at 30 000 units can be expressed as follows:
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FINANCIAL MANAGEMENT
DOL =
contribution (Formula 3.2)
EBIT
DOL =
S – VC
S – VC – F
In the case of Leverage Ltd, this can be calculated as:
30m – 12m
DOL at 30 000 units =
8m
= 2.25
This means, for example, that an increase in sales contribution of 10% will lead to an
increase of 10% × 2.25, that is 22.5% in EBIT. This can be checked against the figures
1
_
produced in Table 3.1. An increase in sales of 33​
% led to an increase in EBIT of
​
3
1
_
75% (33​  3 ​% × 2.25). Assume, now, that Leverage Ltd decides to install machinery which
will increase the fixed costs by R5m and reduce the variable costs by R150 per unit to
R250 per unit. The resulting graphic representation is illustrated in Figure 3.3.
Figure 3.3 Change in fixed and variable costs
From Figure 3.3 it is clear that the break-even point has shifted. It is determined using
Formula 3.1:
15 000 000
Break-even units =
1 000 – 250
= 20 000 units
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The degree of operating leverage will also change if we use the results illustrated below:
Table 3.2 Degree of operating leverage
The EBIT at 30 000 units is lower than it was previously, while at 40 000 units it is higher.
This results from the higher fixed costs and lower variable costs. The DOL at 30 000 units
is calculated as follows:
30m – 7.5m
DOL at 30 000 units =
7.5m
=3
It is confirmed by the fact that an increase of 33​ _31 ​% in sales resulted in an increase of 100%
(33​ _13​% × 3) in EBIT.
Which cost structure is preferable? There is no correct answer to this question. The
original cost structure is less risky as the break-even number of units of 16 667 is easier to
attain than the 20 000 required by the second cost structure. However, as sales increase, a
higher EBIT is obtained using the second cost structure. This is a classical risk/return issue.
The riskier option offers greater potential losses if sales volume is low, but greater potential
profits when sales volume is high. The total business risk is therefore a function both of sales
and costs.
It is worth noting that managers do not have total control over the DOL. Often the
nature of the industry prescribes the extent to which the business must incur fixed costs.
Financial risk
Financial risk results from the practice of financing a part of the firm’s assets with interestbearing debt, with a view to increasing the ultimate return to the ordinary shareholders.
Interest must be paid regardless of the performance of the firm. As a result, a firm which is
liable for fixed interest payments is exposed to a risk of default which is not faced by a firm
financed exclusively with shareholders’ funds.
When the company is experiencing boom sales, the return on assets is likely to be consid‑
erably higher than the cost of the debt. As a result, positive financial leverage is experienced,
which enhances the return on equity. However, in recessionary times the opposite effect is
experienced, resulting in the possibility of defaulting on creditors. The company without
debt is not subject to this risk, as all losses are fully absorbed by the shareholders.
The degree of financial leverage (DFL) arises only after the EBIT has been calculated. It
is identical in concept to the DOL, as it increases fixed costs, being the fixed cost of interest
which must be paid. The formula for determining the DFL is as follows:
DFL =
EBIT (Formula 3.3)
EBIT – I
where: EBIT = earnings before interest and tax
I = total interest expense on all debt
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FINANCIAL MANAGEMENT
Total company risk
Operating leverage and financial leverage work together to create what is referred to as the
degree of combined leverage (DCL). This results from the product of the degree of operating
leverage and the degree of financial leverage and may be expressed as follows:
DCL =
S – VC
(Formula 3.4)
S – VC – F – I
Stated more simply:
Contribution
DCL =
Net income before taxation
DCL can also be stated as: DCL = DOL 3 DFL
Example 3.2:
Table 3.3 shows abbreviated contribution income statements of two companies.
Table 3.3 Income statements
Find the degree of operating leverage, the degree of financial leverage, and the degree of
total leverage for each company. Using the appropriate formulae, the following results are
obtained:
Table 3.4 Degree of combined leverage
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Although both companies have similar sales revenues, it emerges that the net income of
Leverhi is considerably more sensitive to a decline in sales revenue. For example, if sales
revenue declines by 20%, the net income of Leverhi will fall to R13.7m while the net income
of Gearlow will only fall to R20.2m. The converse is also apparent in that an increase in
sales revenue will benefit Leverhi considerably more than Gearlow. Again, this reflects the
typical risk and return relationship. Leverhi is classified as a more risky business operation
because of the greater potential loss in times of economic adversity. However, it has a
greater potential for profit should sales revenue increase.
The use of DCL as a means of assessing risk is useful for the management of a company,
particularly when budgets are being prepared or capital expenditure is being considered.
Investors do not normally have access to this type of information. However, investors do
understand that companies that operate in such sectors as the airline, oil, aluminium,
chemical, shipping, steel, and manufacturing and hotel sectors will be subject to relatively
high levels of operating leverage. These are capital intensive industries requiring significant
investments in airplanes, property, ships, and plant and equipment. High levels of operating
leverage may be accentuated by high levels of financial leverage. Companies that operate in
the retail sector such as Pick n Pay and Foschini may have low levels of operating leverage.
Retailers will however often have fixed commitments in relation to long-term leases.
Investors use mainly stock market indicators to assess risk.
2 MEASURING EXPECTED RETURN AND RISK
An investor is able to measure past returns from investment in a single share with relative
ease. The two components of return are the dividends received and the capital or price
appreciation of the share, expressed as follows:
Rs =
P1 – P0 + D (Formula 3.5)
P0
where: Rs = return to shareholder
P0 = share price at the beginning of the period
P1 = share price at the end of the period
D = dividends received during the period
Depending on the purpose of the calculation, the period may be a week, a month, a year, or
any other period. For the purpose of comparison, annual returns are most useful.
Note that the capital appreciation (P1 – P0) is included regardless of whether or not the
shares were sold and the capital appreciation realised.
Like all decisions, the investment decision depends upon forecasting future events. Past
returns may be a valuable input used in forecasting expected future returns. If, however,
information is available which indicates that conditions in the future will differ from those
in the past, such information must be taken into account when determining the expected
return.
Measuring the expected return on a single share
Expected returns on an investment with an uncertain outcome cannot be accurately
quantified. However, if probabilities can be assigned to a number of alternative outcomes,
it is possible to statistically determine the expected return.
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The probability of an event occurring is the frequency with which that event is expected
to occur relative to all other events. A probability distribution sets out all the possible
events with their expected frequencies of occurrence. Once the probability distribution is
established, it is possible to apply a simple statistical technique in order to provide the
measure of expected return.
Example 3.3: Measuring return
Following extensive analysis and forecasting, you have established that an investment in
Mills Ltd offers the following probability distribution of returns, given different states of
the economy:
Note that the probabilities add up to 100%. Traditionally, probabilities are denoted by
decimals between zero and one. All events are mutually exclusive. These conditions are all
necessary in order to perform a probability analysis. The expected return is determined as
in Table 3.5.
Table 3.5 Calculating the expected return (Re)
The expected return on the investment is 12%. The formula is calculated as follows:
n

Re = ​ ​​​  Pj 3 Rj(Formula 3.6)
j=1
where:
Rj = the jth possible outcome
Pj = the probability of the jth outcome
n = the number of possible outcomes
Measuring risk for a single share
Having earlier defined risk as the magnitude of expected difference between actual outcome
and expected outcome, a commonly used statistic to measure this magnitude is the variance
as calculated in Table 3.6, using the same data as Example 3.3.
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Table 3.6 Calculating the variance
x
Risk may also be expressed as the standard deviation rather than the variance. The standard
deviation is simply the square root of the variance.
 = ​ 2 ​(Formula 3.7)
where:
 = standard deviation
2 = the variance


The standard deviation is ​ 0.0386 ​= 19.65%
The formula for finding the standard deviation from the raw data may be written as follows:


n
=​
j=1
Pj × (Rj – Re)2 ​ ​(Formula 3.8)
where: Pj = the probability of the jth outcome
(Rj – Re)2 = the deviation squared of the jth outcome from the expected
return calculated in Formula 3.6
The mean–variance rule
Once the expected return (measured by the weighted arithmetic mean) and the risk
(measured by the variance or standard deviation) have been established, a general rule
becomes apparent. It is commonly referred to as the mean–variance rule and is applicable
to all investment decisions made by rational risk-averse investors. The rule holds that
investment A will be preferred to investment B provided one of the following two conditions
exist:
■■ either the mean expected return on investment A exceeds that of investment B and the
variance of A is equal to or less than that of B,
■■ or the mean expected return on A exceeds or is equal to the expected return on B and
the variance of B is greater than that of A.
It has given rise to the technique of mean–variance analysis, which is a widely-used way of
making investment decisions. The rule is applicable to all risk-averse investors, regardless
of the degree of their risk aversion, and is illustrated in Figure 3.4.
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Figure 3.4 The mean–variance rule
The following can be seen from Figure 3.4:
■■ Investments W and X are always preferred to investments Y and Z respectively as they
offer superior returns for the same risk in each case.
■■ Investment X is superior to investment Y because it offers the same expected return but
is subject to less risk.
The mean–variance rule can now be applied to relevant investments. The measure of risk
which will be used in this text will be the standard deviation (the square root of the variance)
as it is more commonly used and is more easily applied to statistical manipulation arising
from the normal distribution to be discussed in the next section.
3 INTERPRETING THE SUMMARY STATISTICS
The expected return is simply the weighted average of each return predicted for a given
state of the economy. The risk associated with the expected return is measured by the
standard deviation of the return. The facts provided in Example 3.3 could be graphed as
in Figure 3.5.
Figure 3.5 depicts a discrete probability distribution. Five mutually exclusive states of the
economy have been identified. In fact, there are numerous possible states which could exist,
each of that could be assigned a probability. The result could be graphed as a continuous
probability distribution.
Properties of a normal distribution
Past company returns may follow a normal distribution. This means that in general they are
symmetrically distributed around a central value, with decreasing frequency of occurrence
as the distance above or below this central value increases.
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Figure 3.5 Probability distribution of Mills Ltd rates of return
Using the data of Mills Ltd, a continuous probability distribution could be roughly drawn
using the known characteristics of the normal distribution. From Figure 3.5 it is not absolutely
apparent that the distribution has the characteristics of a normal or Gaussian distribution.
The normal distribution was first investigated in detail by the German mathematician
Gauss. Its properties can be applied when results tend to be symmetrically distributed
around a central value with increasing rarity of occurrence as the distance away from the
central value increases. Where only five discrete probability states have been identified, the
resulting histogram may not appear symmetrical. This is largely a result of the small number
of discrete probability states and does not detract from acceptance of normal distribution
characteristics as the basis for determining the descriptive statistics. The most important
properties of the normal distribution for an understanding and interpretation of risk as we
have defined it are:
■■ Half the area under a normal curve is to the left of the expected return and half is to the
right. This means that the curve always peaks at the expected return.
■■ Standard deviations demarcate points that cover the following area under the normal
distribution curve:
– Between +1 and –1 = 68.3%
– Between +2 and –2 = 95.5%
– Between +3 and –3 = 99.7%
Using the standard deviation as the unit of measurement, it is possible to establish the area
under the normal curve at any point by referring to Table E, at the end of the book. This will
be explained later in the chapter.
These facts, together with the summary statistics obtained for Mills Ltd, are illustrated
in Figure 3.6 from which the following observations can be made:
■■ The curve peaks at 12%, the expected rate of return. There is therefore a higher
likelihood of a return of 12% than of any other return.
■■ There is a 68.3% chance that the return will be between –1σ and +1σ. Because the
standard deviation has been calculated to be 19.65%, this means that there is a 68.3%
chance that the expected return will be between –7.65% (12% – 19.65%) and 31.65%
(12% + 19.65%). Conversely, there is a 31.7% chance that the return will be outside
this range. As risk is the possibility that the outcome will be worse than expected, the
chance of the return being below –7.65% is only half of 31.7%, that is 15.85%.
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Figure 3.6 Continuous probability of Mills Ltd’s rates of return: normal distribution
■■
There is a 95.5% chance that the actual return will fall between +2 and –2 that is,
between 51.3% (12% + 2 × 19.65%) and –27.3% (12% – 2 × 19.65%). Looking at the
adverse side of the risk, we can say that there is a 2.25% chance, (half 100 – 95.5%), that the
actual return will be below –27.3%. Similar numbers can be generated for the range –3 to
+3.
Comparison of single shares
We have focused on the summary statistics relating to a single investment opportunity.
When faced with alternative investment opportunities, the investor who wishes to make a
choice between two single investment opportunities needs some rationale on which to base
the decision process. The strategy that should be adopted is illustrated in Examples 3.4 and
3.5 which follow.
Example 3.4: Choosing between two alternatives: identical expected returns
A financial analyst has gathered information regarding the performance of two listed shares
over the last five years. Trinpak is listed under the paper and packaging sector, and Claycor
under the building and construction sector.
The following summary statistics are generated:
Trinpak Claycor
Return to shareholders
22.0%
22.0%
Standard deviation of return
9.2%
15.4%
In this case, past performance may be used as a surrogate for expected future returns. Given
that the expected return is identical for both investment alternatives, on what basis is a
choice between the two alternatives made?
These two alternatives are represented in rough graphs in Figure 3.7.
It is immediately apparent that Trinpak has a much tighter distribution of returns. The
probability of performing really badly, if past performance is used to predict the future,
is much lower than that of Claycor. Faced with these two alternatives, it is likely that an
investor would rather invest in Trinpak Ltd than Claycor Ltd. This is consistent with the
mean–variance rule which implied that, in general, investors will select the alternative with
lower risk when the expected returns are identical.
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Figure 3.7 Distribution of returns: identical expected return
With investors showing a preference for Trinpak on the basis of the facts outlined, what is the
likely result? The greater demand for Trinpak is likely to force its price upwards. Conversely,
the lesser demand for Claycor would place downward pressure on its price until an equilibrium point, where return commensurate with the risk establishes the market price.
When comparing shares which have different expected returns, the decision is more
complex. Looking at the above distributions an investor could surmise that Trinpak has the
characteristics of a defensive stock e.g. a bank, insurance company, healthcare company or
utility. These stocks are preferred during times of uncertainty and recession. Claycor, on the
other hand, is not unlike a resource stock where the returns are poor in times of recession
and high during a boom. A rush into resource stocks at the expense of more defensive stocks
is a signal that an upturn in the world’s economy is expected soon. The probability factors
used in this chapter may have been skewed towards a more optimistic outcome.
Example 3.5: Selecting between two alternatives: different expected returns
An investor is considering the following two alternatives from which to select the most
acceptable investment:
Atlas Ltd Brenco Ltd
Expected return
28%
20%
Standard deviation
14%
8%
Which investment should be selected?
This problem does not have a ready answer. The distributions are depicted in a rough
graph in Figure 3.8.
It is apparent that Brenco Ltd offers a lower expected return, but this is not surprising as
the degree of risk is lower than that of Atlas Ltd.
If an investor wishes to choose between these two shares, some basis of comparison is
required. Using the properties of the normal distribution, two indicators, the co-efficient of
variation and the z score, may be used.
Co-efficient of variation
The co-efficient of variation (CV) relates the units of return to the units of risk. It expresses
the units of risk per 1% of return as follows:
CV =
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Figure 3.8 Distribution of returns: different expected returns
Using the CV, the following results are obtained for Atlas and Brenco:
CV
Atlas
Brenco
14/28 = 0.5
8/20 = 0.4
The results indicate that Atlas Ltd exposes the investor to 0.5 units of risk for each expected unit
of return, while Brenco exposes the investor to only 0.4 units of risk for every unit of return. On
a relative basis, therefore, Brenco seems to offer a better trade-off between expected return and
risk. Note that this approach is not rigorous and serves only as an additional indicator to assist
investors when selection between two alternatives with different expected returns is required.
The z score
The z score is used to help establish the probability of a return falling below a given level.
For example, an investor may wish to determine the probability of the returns being zero or
less. The following procedure would be adopted.
First, find the z score using the following formula:
_
– ​x​​
z = ____
​ x 
where:
x = the given rate being examined
–x = the expected return (the mean)
 = the standard deviation
(Formula 3.10)
Consult Table E – the standard normal distribution (at the end of the book) – and determine
the area to the right of 0% by reading from the table. The figure obtained is the probability
of returns falling between 0% and the mean. Then interpret the results.
Using the z score, the following results are obtained for Atlas and Brenco:
Atlas
Brenco
Z score at 0% 0 – 28 = –2 0 – 20 = –2.5
14
8
Table reading
0.4772
0.4938
% Probability (0.5 – Table)
2.28%
0.62%
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Note that Table E is constructed for only one side of the symmetrical curve, as a z score
table for the mirror image side would be identical. In order to establish the probability of
returns being less than zero, the table reading is deducted from 0.5 (the left-hand side of the
distribution with which we are dealing). The probability is then expressed as a percentage.
This is illustrated for Atlas Ltd in Figure 3.9.
Figure 3.9 Using z scores
This approach once again does not provide perfect information, but allows investors to
develop perceptions regarding the risk/return relationship.
It should be clear that 0% return is a critical point because once returns fall below this
point the investor suffers not only a zero return on capital but also a loss of capital invested.
Investors may, however, be sensitive to other points in the operation of probable returns.
If, for example, an investor wishes to establish the probability of returns being below 15%,
exactly the same procedures are followed.
Atlas has a lower probability than Brenco of generating returns below 15% and (as is
apparent from the earlier calculation) it has a higher probability of returns below 0%. These
indicators are consistent with expectations regarding risk and return.
Atlas
Brenco
Z score at 15% 15 – 28 = – 0.93 15 – 20 = – 0.63
14
8
Table reading
0.3238
0.2357
% Probability (0.5 – Table)
17.62%
26.43%
We can use the Excel function =NORMSDIST to determine the standard normal
cumulative distribution function rather than employ Table E. For example, if you enter
=NORMSDIST(-2) in an Excel worksheet cell, the result will be 2.28%.
We can use the =NORMSINV function in Excel to indicate the number of standard deviations
from the mean which matches a given confidence level. For example, =NORMSINV(0.0228)
will come up with an answer of –2 standard deviations.
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Co-variance and correlation
Co-variance measures how share returns move together and specifies the strength of the
relationship between share return movements. It indicates the extent that share returns
co-vary. For example, we would expect that the share prices of resource companies would
move together. In general, if the share price of Gold Fields goes up, then we would expect
the share price of Harmony also to increase. The share prices of these companies tend to
co-vary.
Mathematically, the co-variance between x and y is denoted as follows:
1
Cov(x,y) = ​ 
n​
n
_
_
​​  (x – ​x​x​)(y – ​​y​y​)(Formula 3.11)
i=1
i
i
where n is the number of observations.
If share returns tend to co-vary, then the actual returns will tend to be above or below their
means for the same period and the product of this relationship will be positive. If share
returns move in opposite directions, then the co-variance will be negative.
Cov(x,y) > 0, x and y will tend to move in the same direction
Cov(x,y) < 0, x and y will tend to move in opposite directions
Cov(x,y) = 0, x and y are independent. There is no relationship between the returns of x and y.
What does co-variance indicate? It is a number and it is difficult to interpret on its own.
We use the correlation co-efficient, xy, which is a standardised version of the co-variance,
to determine the relative strength of the linear relationship between x and y. We need the
covariance to determine the correlation co-efficient which is denoted as follows:
Cov(x,y)
rxy = ​  
  ​(Formula 3.12a)
x
y
The correlation co-efficient is between –1 and +1. A correlation co-efficient of (+1) indicates
that share returns are perfectly correlated. This means that a (+10%) share return by x is
matched by a (+10%) return by y. If the share return of x is (–10%), then the share return
of y will also be (–10%). A correlation of (–1) indicates that shares are perfectly negatively
correlated. Therefore a (+10%) share return by x is matched by a (–10%) return by y.
We can restate the above formula as follows:
Cov(x,y) = rxysxsy(Formula 3.12b)
How do we calculate the co-variance? We will use the example set out in Table 3.7 and do
it the long way before simply using the relevant Excel functions. We will come back to this
example in Chapter 4 on Portfolio Management. Why is co-variance important from a risk
perspective? If the returns of investments do not co-vary, it means that portfolio risk will be
lower than if the returns do co-vary. We will expand more on this in Chapter 4.
In Table 3.7, we have two shares P and Q which offer the returns as set out in the table for
each year. We calculate the mean return for P and Q and then set out the difference between
the return
_ and_ the mean for each observation, to comply with part of the above formula,
i.e. (x – ​x​)(y – ​y​). We then sum the product of the differences and calculate the average of
the product to determine the co-variance. We can use the Excel functions, COVAR (array
1, array 2) and CORREL (array 1, array 2) to determine the co-variance and the correlation
co-efficient.
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Table 3.7 Co-variance and correlation
We have used the Excel functions to support the calculations. Note that we have determined
the co-variance by using percentage returns. If using absolute numbers, the co-variance
would be 127, but the correlation would remain at 97.8%. We will come back to this example
in Chapter 4.
Value at Risk (VaR)
VaR answers a simple question. How much can a firm lose over a period of time (such as
a day), under normal market conditions and subject to a given probability. A portfolio with
a one-day 5% VaR of R50m means that there is a 5% probability that the portfolio will
fall by more than R50m in any one day. Value at Risk is a useful risk management method
used by banks, financial institutions, firms and investors to manage exposure to losses.
Although volatility is useful to measure risk, it includes downside and upside movements
as volatility indicates dispersion around a mean. Investors are not as concerned by dramatic
upward movements in prices or returns although it is important to determine whether such
movements are supported by improvements in operating performance. Although Warren
Buffett’s Berkshire Hathaway share price has been volatile, this was mainly due to dramatic
upside movements in the share price. Investors are much more concerned about losses and
about measuring a worst-case scenario. Investors wish to know the probability of losing money
and VaR is a useful risk management tool that includes three aspects; a time period like a day,
month or year, a 95% or 99% level of confidence and a specified investment loss stated either
in monetary terms or as a percentage. In practice, managers will often estimate 5% VaR.
Let’s use an example and real financial data to explain VaR. An asset manager wishes to
evaluate investing in emerging markets rather than investing in the USA but is concerned
about downside risk and wishes to apply a 5% VaR. The average monthly return of investing
in emerging markets from January 1988 to May 2018 was 0.882% per month and the standard
deviation was 6.52%.
In terms of the normal distribution, the one-tail 95% VaR is equivalent to 1.645 standard
deviations from the mean3. If the distribution of emerging market returns is normal, then we
could determine the VaR as follows:
VaR = Mean – (1.645 × Standard Deviation) = 0.882% – 1.645 × 6.52% = –9.84%
If we apply =NORMSINV(0.95) in Excel for a 95% confidence level, then the answer is 1.645 standard
deviations. Otherwise, apply =NORM.INV(0.05,0.00882,0.0652) to determine VaR of -9.84%.
3
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Therefore, there is a 95% probability that monthly returns will be above –9.84% and a 5%
probability that monthly returns will be equal to or worse than –9.84%. This means that the
asset manager can expect a negative monthly return of at least –9.84% once every 20 months
(1/20 = 5% of the time).
We can also determine VaR by ranking the historical data, assuming that the historical
returns are representative of what could occur in the future. There are 365 months of returns
between January 1988 and May 2018 and 5% of 365 is 18.25. If we rank the MSCI Emerging
Markets’ monthly returns from lowest to highest returns, then the lowest 19 monthly returns
with associated months are as follows:
The 5th percentile is between -10.694% and -10.282% and we use Excel to determine this to
be -10.57% [=PERCENTILE.EXC] 4. This is based on actual data and is a larger loss than
the projected loss of –9.84% assuming a normal distribution. It is likely that market turmoil,
disruptions and meltdowns are more common than indicated by a normal distribution. This
is referred to as “fat tails” to describe the distribution and our results for emerging market
returns support this assertion to some degree. In practice, there are more likely to be fat left
tails implying a higher degree of significant losses than predicted by the normal distribution5.
VaR is a useful indicator of downside risk as in this case we can expect worse than a –10.57%
return, 5% of the time which is about once in 20 months. The asset manager is now aware
that he or she has a 5% chance of losing more than 10.57% in any single month. It is also
true that –10.57% is the most optimistic loss and it does not capture a worst-case scenario.
Expected Shortfall
VaR reports the most optimistic measure of risk by reporting the smallest loss. It may be
more realistic to report what the expected loss would be within the 5% range of worst
possible returns. This is called the expected shortfall and we assume an equal probability
for each negative return falling within the 5% most negative returns range. If we sum the
lowest 18 returns set out above plus 0.25 of –10.282% and then divide by 18.25, we can
determine an expected shortfall of –14.819%. This is a significantly greater loss than the
negative 10.57% return disclosed with VaR. This is also called conditional tail expectation or
conditional value at risk.
The distance between –10.694% and –10.282% = 0.412% and we multiply this by 25% to get to 0.103% and
then we add this to –10.694% to get to an approximate value of –10.591%. More accurately, we should use 5% x
366 [n+1] = 18.30 and 0.30 x 0.412% = 0.124% so that -10.694%+0.124% = –10.57% We can also use the Excel
function =PERCENTILE.EXC(F38:F402,0.05) where you specify the data range (in our case this was F38 to
F402) and the 5th percentile. Excel will indicate the return below which 5% of the returns are. Excel calculates this
to be –10.57% for emerging markets and –7.1% for developed markets.
5
Kurtosis measures the likelihood of extreme values from the mean and therefore the likelihood of fat tails. A
Kurtosis score above zero (excess Kurtosis) will indicate fatter tails than indicated by a normal distribution. If we
employ the Excel function, =KURT, to our data set (LN returns), we find that the Kurtosis is 3.38 which indicates
the existence of fat tails.
4
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Figure 3.10 reflects all the monthly returns ranked from lowest to highest returns which is
interesting as it indicates that there were 145 months in which emerging markets reported
negative monthly returns. Again, this is a further useful indicator of risk.
Figure 3.10 Emerging markets monthly returns ranked from lowest to highest: 1988–2018
Conclusions
Another way of determining VaR is to apply Monte Carlo simulation and we will explain
the use of Monte Carlo simulation to evaluate the risk of capital projects in Chapter
10. We will come back to emerging markets later in the chapter. In this section, we have
explained the use and purpose of VaR to indicate the probable monthly loss we can
expect to experience 5% of the time. In order to manage downside risks, it is useful
for an asset manager to know that there is a 5% chance that in any month the firm
could experience a loss greater than –10.57% (or an expected shortfall of –14.59%)
when investing in emerging markets. How does this compare to investing in a developed
market like the USA? We will come back to this question later in the chapter.
Historical returns
When we determined an expected return in Example 3.3, we projected possible future
returns and associated probabilities. When we analyse historical returns, we are simply
given realised returns and time periods and we assume an equal likelihood for each period’s
return. This means that in order to determine an average return, we simply assume a 1/n
probability of each return. Therefore, we can determine an arithmetic average by dividing
the sum of returns by the number of periods. If the actual returns for years 2017 to 2019
were –20%, +40% and +10%, then the average annual return is 30%/3 = 10% and we
implicitly assume that there is a 1/3 probability of each return occurring.
We can also use a compound annual growth rate6 (geometric average) to explain market
returns. When we report that a company’s share price of R100 went up by 10% in the first
year and then by another 30% in the following year, we normally apply a multiplicative
factor so that at the end of Year 2, we would expect the share price to be R100×1.10×1.30
The use of the term compound annual growth rate (CAGR) has become a standard way of describing a geometric
average. It may not need to refer to an annual period and we will also refer to the terms “compound average growth
rate” and “compound annual return” to depict a geometric average.
6
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= R143. We will further assume in our example that the share price at the end of Year 3 is
R133.10 so that the share prices and related returns are set out below:
In the case of share returns and other series that involve compounding, the geometric average
(compound annual growth rate) may be more appropriate than an arithmetic average.
Although the arithmetic average is 11.026%, the compound annual return is computed to
be 10% [(133.1/100)1/3 –1 = 10%]. We can also set this out as the nth root of the product of
1+return for each year, as follows:
1
__
CAGR = (​​ (1 + R1)(1 + R2)…(1 + Rn) )​ ​​n ​​– 1
(1.10 × 1.30 × 0.93077)1/3 – 1 = 10%.
(Formula 3.13)
If we multiply our investment of R100 by a factor of 1.10 each year, we will achieve a value
of R133.10 by the end of Year 3. In Chapter 2, we explained compounding and the formula
of FV = PV(1+r)n. We are essentially using this formula to determine the compound annual
growth rate (geometric average) as follows:
Ending value = Beginning value(1+r)n
(Ending value/Beginning value)1/n = 1+r, so (133.10/100)1/3 = 1.10
What about dividends? Assume our company paid a dividend of R7 in Year 1 and a dividend
of R10 in Year 2. No dividend was paid in Year 3. How do we compute returns? It is important
to include the reinvestment of dividends in order to compare returns of companies and to
compute the total shareholder return (TSR) that the company achieved per year. We assume
that the dividend is paid at yearend and we use the dividend to purchase shares, so that the
dividend of R10 in Year 2 will be used to purchase 0.06993007 (R10/R143) of one share for
every share held at the end of Year 2. If we start with one share at the end of Year 0, then the
value at the end of Year 3 will be R150.88.
We have been able to purchase 0.06363636 shares in Year 1 and 0.06993007 shares in
Year 2 with the dividends, which means we will have 1.13356643 shares at the end of Year 3.
The shares, prices and values are set out as follows:
Value at end of Year 3: 1.133566 shares  R133.10 = R150.88
Compound annual return = (150.88/100)1/3 – 1 = 14.69%
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The arithmetic average returns based on changes in the prices and changes in the values of the
shares (with the reinvestment of dividends) are as follows:
The compound annual return is lower than the arithmetic average return. We have computed
annual returns. However, we can compute the holding period return which represents the
total return over a period of time. For example, the holding period return in our example is
50.88% over the three-year period.
The compound annual return based only on price movements is 10% per year which
assumes that dividends are not reinvested. If we include the reinvestment of dividends,
then the compound annual return will increase and this incremental return due to the
reinvestment of dividends is significant over long periods.
Let’s go back to arithmetic average returns and compound annual returns. Which average
is better? The compound annual return better describes the long-run performance of an
investment. This is the actual return we earned from Year 0 to Year 3. If we wish to compare
investments, then it is more relevant to use compound annual returns and this is what
unit trusts, mutual funds and Warren Buffett use to set out relative investment returns.
Arithmetic average returns are always higher than geometric returns due to volatility. Yet,
the arithmetic mean can be useful as an unbiased predictor of next year’s return. We have
written more about the nature of returns in Appendix 3.1 whereby we demonstrate why
compound returns are more reliable and accurate from an investment perspective than
arithmetic average returns.
4 RISK AND RETURN IN FINANCIAL MARKETS
In this chapter, we have noted that investors will demand a higher return for taking on a
higher level of risk. If a government bond is offering an expected return of 6% per year, then
we would demand a higher return for investing in corporate bonds and an even higher return
for investing in ordinary shares. Why? A company’s earnings are subject to greater economic
risks and share prices can be volatile. The additional return that investors will demand for
investing in ordinary shares rather than government bonds is called the equity premium
or the market risk premium. We will come back to the equity/market risk premium in
Chapter 7. In this section we would like to understand whether, historically, ordinary shares
have offered higher returns than government bonds. The question of whether investors
have been rewarded for taking on the additional risks of being invested in ordinary shares is
important as the risk/return relationship is critical to the theory of finance.
In South Africa, investors in ordinary equities earned a real return of 7.3% per year over
the period 1900 to 2017, a period of 118 years. A real return is what you earn after deducting
inflation. Investors in bonds earned a real return of 1.8% per year over the same period. Over
the period 1900 to 2016, South African equities earned a real return of 7.2% per year and
bonds earned a real return of 1.8% per year. We will focus on this 117-year period as we have
data for other countries. You will note from Table 3.8 that South Africa offered the highest
equity returns in the world over the period 1900 to 2016. Equities in the USA offered a return
of 6.4% per year while Germany offered a return of 3.3% only. Equity returns in Russia and
China were deeply affected by war and revolution, which resulted in expropriation and we
have therefore not included these countries in Table 3.8, which sets out the real returns for
equities and bonds.
It is interesting to convert these returns into cumulative real returns for each country.
One Rand (or equivalent) invested at the beginning of 1900 in ordinary equities would
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have grown to R3 410.37 in real terms while R1 in bonds would have grown to only R8.1
in real terms. This is a big difference and reflects the power of compounding. These
accumulated sums tell the real story of investing over long periods of time. The extra 5.4%
(7.2 – 1.8) return per year offered an investor an increase of R3 402.2 (3 410.3 – 8.1) on
the R1 investment compared to a bond investor who accumulated R8.1 only. Table 3.8 also
discloses real returns for a shorter period from 1967−2016, which is 50 years. In the latter
period, South Africa was second to Sweden with respect to equity returns.
Table 3.8 Real returns for equities, bonds and bills
We would expect that equities should offer higher returns than bonds as equities involve
higher levels of risk and bonds should offer higher returns than bills as bonds are subject
to price volatility. The evidence in Table 3.8 is clear. Equities have outperformed bonds for
each country and each period (except for Italy over the period 1967 to 2016) and bonds have
outperformed bills for each country and for each period (except Portugal for the period
1967 to 2016).
What about other periods? Table 3.9 presents the compound annual returns from
investing in the All Share Index (ALSI), Bonds and Cash (Money Market Index) over the
period 1987 to early 2010.
Table 3.9 Returns for equities, bonds and cash in South Africa
7
How did we work this out?
Equity: FV = R1 × (1.072)117 = R3410.3
Bonds: FV = R1 × (1.018)117 = R8.1
Please note that there are slight rounding differences in terms of the Credit Suisse returns indicated in Table 3.8.
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The nominal return from investing in equities is higher than investing in bonds and cash –
but not by much – resulting in a market risk premium of 1.43% that is much less than
over the period 1900 to 2017. We will explain what the Sharpe ratio means later in the
chapter.
What about risk? Do investors earn higher returns for undertaking higher levels of risk?
Table 3.10 presents the returns from investing in equities and bonds and the associated
volatilities as indicated by the standard deviations for each country and asset class. Equities
on average do earn higher returns than bonds and bills/cash but also report higher levels of
volatility.
Table 3.10 Real average returns and associated standard deviations
The geometric average returns for equities exceed the geometric average returns for bonds
and the same is true for arithmetic average returns. The higher relative volatility of equity
returns relative to bond returns is reflected in a much higher standard deviation for world
equities of 17.4% as compared to 11.2% for world bonds. The standard deviation for South
African equities is 22.1% whilst the standard deviation for bonds is 10.5%. Although not
disclosed in Table 3.10, the standard deviation for South African bills is 6.1% as compared
to an arithmetic return for bills of 1.2%. The measures of volatility support the premise that
we would expect higher returns from equities in relation to bonds and higher returns from
bonds in relation to bills. Although there have been specific periods whereby bonds have
outperformed equities, generally lower returns are aligned to lower volatilities.
Figure 3.11 determines the accumulated amounts in real terms from investing R1 in 1900
(or one year before 1900) in equities for selected countries. The annual compound returns
in Table 3.8 do not adequately capture the differences in real accumulated values from
investing in equities and reinvesting all income over 117 years.
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Figure 3.11 Cumulative amounts stated in real terms from investing 1 unit of local currency in equities (and
reinvesting all income) from 1900 to 2016
In real terms, after inflation, investing R1 in 1900 would result in an accumulated amount
of close to R3 410 by the end of 2016. If your great-grandfather had invested R1 000 in
equities in 1900, and had bequeathed this to you, you would have received R3.410 million
at the beginning of 2017. Yet, to be fair we should also include currency effects. Figure 3.11
depicts returns and accumulated amounts in each country’s own currency.
When we take into account the fact that the Australian Dollar and the US Dollar have
appreciated against the Rand, then Australian investors and USA investors have done better
than South African investors. In fact, we often refer to Rand hedges, which are shares that
should protect investors against any depreciation in the Rand and the JSE’s market capitalisation
is dominated by groups such as MTN, BHP Billiton, BAT, and Naspers that have significant
international operations.
Figure 3.12 presents the cumulative returns of investing R1 in either the JSE ALSI,
Bonds or Cash over the period between January 2004 and March 2018.
Although equities have been more risky, the returns to investors have been significantly
greater than that of bonds and cash.
In another study by Professor Brian Kantor of Investec Securities Research, the mean
return for the JSE ALSI (All Share Index) was 15.29% for the period January 1970 to
July 2005 whilst bonds offered an annual return of 11.9%. The results are presented in
Table 3.11. We have updated this to 2018. Investing in equities was much more risky and
offered higher returns. However, although bonds implied higher levels of risk, they offered
marginally better returns than an investment in cash over this period. Investors in equities
were also required to accept significant annualised falls in equity prices in some months.
Accepting the upside was no problem (if you were invested) but it was necessary to live
through the reversals in values as well.
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Figure 3.12 Investment of R1 in either equities, bonds or cash in Jan 2004, with reinvestment of income
until March 2018
Source of data: Prof. Brian Kantor – Investec Securities
Table 3.11 Nominal annual returns and standard deviations
Have equities always outperformed bonds? It depends on our starting date. In South Africa,
bonds actually outperformed equities from 1990 to May 2005. That is a long time.
What about small companies? In the USA, since 1926, investing in “small value caps”
offered investors an additional return of 3.6% per year. The MSCI Small Company Index
from 29 December 2000 to 31 May 2018 has offered an annual return of 9.75% per year
which is 4.06% higher than the annual return offered by the MSCI USA Index. From 1990 to
2010, the excess mean return for small caps in South Africa was found to be between 1.98%
and 3.24%, relative to large market cap firms8.
See Auret and Cline (2010). Size and value investment strategies on the JSE, Conference Paper presented at the
African Finance Journal Conference, Stellenbosch, 2010.
8
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Let’s compare the volatilities of different sectors. We will select the general mining sector
and the food producers sector. Anglo American plc is a key component of the general
mining index and Tiger Brands is a key component of the food processors index. We have
determined the monthly percentage changes in the general mining and food processors
indices. This is presented in Figure 3.13.
Figure 3.13 Monthly percentage changes in the Mining and Food Producers Indices: May 2004–April 2018
We can clearly see that the Mining Index is more volatile than the Food Processors Index
over the period. Therefore, if we are investing in companies that form part of the Mining
Index, we need to be prepared to accept the additional volatility and risk that comes with
investing in these companies. The standard deviation of the General Mining Index was
7.84% per month whilst the standard deviation for the Food Producers Index was only
4.34%.
Let’s evaluate the share price movement and volatility of Anglo American plc which is
a company that forms part of the General Mining Sector on the JSE. The group is one of
the world’s leading resource companies and Figure 3.14 depicts the movement in Anglo
American’s share price from June 2006 to April 2018.
The movement in share price initially reflected the increase in commodity prices that was
driven by Chinese demand. Then the economic crisis struck in the latter half of 2008 and the
share price fell sharply from a high of R548 in June 2008 to R141 within a period of eight
months. Although recovering in 2011, the price of Anglo American collapsed and hit R63 in
January 2016 due to concerns about significantly lower growth in China, and the potential
fall in demand for resources going forward.
The dramatic fall in Anglo American’s share price indicated the risks of investing in
equities. Although equity markets have recovered, we can see that the share price in April
2018 has only come back to levels applicable in June 2006.
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Figure 3.14 Movement in the Anglo American share price: June 2006 – April 2018
When we plot the share price, we do not obtain a clear picture of the underlying volatility
in Anglo American’s share price. In Figure 3.15, we plot the monthly percentage changes in
Anglo American’s share price over the same period.
Figure 3.15 Monthly percentage changes in the Anglo American share price: July 2006 – April 2018
The graph of changes in the share price indicates the increased volatility around the time of
the economic crisis. Greater volatility in the share price occurred during 2015 to 2017 due
to lower economic growth in China, market turmoil and a significant fall in the oil price and
then subsequently by the strong recovery in the global economic outlook. Over the period,
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the standard deviation was 11.814% per month which was higher than the standard deviation
of the General Mining Index. This means that 68.3% of the monthly percentage changes in
the share price were in the range of 211.150% to +12.478% (0.00664 – or + 0.11814). The
average monthly return was 0.664%. If you invest in equities then you do need to accept the
associated volatility in returns. However, the evidence indicates that investors (over the long
term) do earn higher returns for accepting the higher risks of investing in equities.
Emerging markets
The growth in emerging markets and capital flows to emerging markets has been phenomenal.
Whether this will be sustained is an open question, but future growth will mainly occur in
emerging markets such as China, India and Brazil. Emerging markets is also where 70% of the
world’s population lives and South Africa is an emerging market. Emerging markets produced
an annualised return of 10% per year in the decade to 2010 whilst for the developed world; this
was close to zero. However, in the three years to October 2014, emerging markets reported
lower returns than developed markets. Yet, despite this, Dimson, Marsh and Staunton of
London Business School write in the 2014 Credit Suisse Global Investment Returns Yearbook
that “from 2000 to 2013, the terminal wealth accruing from investing in emerging markets was
almost twice that from an equivalent investment in developed markets.” From early 2016 until
February 2018, emerging markets staged a significant rally in relation to developed markets,
which also performed strongly. Figure 3.16 sets out values based on the MSCI indices for
emerging markets and developed markets (MSCI World Index) since 1987. The relative
outperformance of emerging markets is significant. An investment of $100 in 1987 would
have grown to $1 120.71 by 3 June 2018, whilst the same investment of $100 in developed
markets would have grown to $508.77.
Figure 3.16 Emerging markets and developed markets: performance from 31 December 1987 to 3 June 2018
What about risk? Emerging markets have always been seen as more risky. Is this true? The
emerging markets index has generally been more volatile and emerging markets reported an
annualised standard deviation of 23% over the 30.5 years to 2018 as compared to developed
markets which reported an annualised standard deviation of about 15%. The beta of emerging
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markets to developed markets is 1.309. Investors should expect higher returns from investing
in emerging markets as there is more risk there.
Table 3.12 presents summary statistics for emerging markets and developed markets. The
higher relative arithmetic average and compound average returns reflect the higher risks of
investing in emerging markets. We have included a Value at Risk measure (by applying the
=NORMDIST Excel function) and the data indicates that there is a 4.77% chance of losing
more than 10% in any one month by investing in emerging markets but there is only a 0.68%
chance of losing more than 10% in any one month by investing in developed markets.
Table 3.12 Summary statistics for emerging markets and developed market returns Jan 1988 to May 2018
From a diversification perspective, investors can reduce the risk of their portfolio by investing
in both developed markets and emerging markets. We will come back to the issue of
diversification and risk in the next chapter.
Volatility and time periods: the Rip van Winkle solution to risk
Volatility is often time dependent. The shorter the time interval, the greater the volatility
will be on an annualised basis. Annual holding periods generate greater volatilities than
5-year or 20-year holding periods. A study by Firer and Staunton (Investment Analyst
Journal, 56, 2002) found that an annual holding period resulted in a standard deviation
of 23% for equities. However, as we increase the investment period and evaluate a 5-year
holding period, we find that there is a significant fall in the standard deviation to 9.9%.
If we follow the Rip van Winkle solution to risk and fall asleep for 20 years, then we will
find that the standard deviation for a 20-year holding period is only 5.5%. If you invest for
20-year holding periods, then equities have always out-performed bonds. The markets have
offered maximum positive real returns of close to 100% and negative real returns of close to
–60% over a one year holding period. Over a 5-year holding period, the maximum positive and
negative returns are 20% and –20%. Over a 20-year holding period, the maximum real return
is about 12% and the maximum negative return is close to zero. If we go back to Figure 3.14, if
you had invested in Anglo American in June 2006, went to sleep and you only woke up in April
2018, you would have looked at the share price and it would have hardly moved. You would
have missed a roller coaster ride of volatilities and price movements.
What does Warren Buffett think?
According to Buffett, volatility is not a valid measure of risk and an investor should try
to rather understand the business and the volatility inherent in the business. The risk
that counts is not beta but the possibility of permanent loss. The quality of the business
9
Credit Suisse Global Investment Returns Yearbook, 2010.
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determines the level of risk. The competitive strength of Coca Cola and Gillette (now part
of Proctor and Gamble) reduces the risk of investing in these companies relative to other
companies that do not have a sustainable competitive advantage but may have similar betas.
What do we think? We think that the importance of volatility may be overstated and we
agree that a more relevant measure of risk relates to the probability of failure. We will come
back to this when we evaluate project risk in Chapter 10 and we focus not only on measures
of volatility but also on the strategic context of an investment. Yet our view is also more
nuanced. Why? We consider that volatility may be relevant for determining the probability
of business failure. It depends on the company.
Firstly, let’s assume a company is mining and producing platinum and the company has
high levels of debt. Platinum prices have been volatile and therefore the company’s share
price has also been volatile. Even though the market is expected to recover, the banks may
force the winding up of the company before markets are able to recover. If the share price
is undervalued at that point, then the company may not be able to raise equity finance to
prevent bankruptcy. Remember that the company is expected to recover but due to price
volatility and fixed borrowing costs and fixed operating costs, the company is incurring
losses. A company with little debt is far less likely to fail as it does not have to meet fixed
borrowing costs or arrange debt refinancing in volatile times. Corporate survival is the key
factor as this enables a company to be around to take advantage of investment opportunities
when the market does recover. The question we should ask is whether volatility endangers
the existence of a company. If not, then volatility may not be that important.
Investors like Warren Buffett in fact welcome volatility as it offers opportunities to
purchase good businesses at distressed prices. This does not mean that there is no risk – at
least for investors who are forced to sell in a time of volatility due to pressure, placed by
the lenders. However, we also agree that there is much more to risk than simply evaluating
volatility, particularly volatility over short time intervals. We will come back to the issue
of volatility and risk in Chapter 10. We need to understand that Buffett does not like
debt financing. Yet betas are affected materially by the level of debt financing. A highly
geared company will tend to have high betas. We will analyse the impact of debt on betas in
Chapter 7. Buffett also does not believe necessarily in diversification although in this case
his company, Berkshire Hathaway, does hold a diversified portfolio. The expression, “Don’t
put all your eggs in one basket’ is replaced by Mark Twain’s alternative advice: ‘Place all
your eggs in one basket but watch that basket”.
Risk-adjusted measures of performance
In Table 3.10, equities offer higher returns but also higher volatility than bonds and bills.
However, the question is whether returns are enough to offset the additional risks of equities.
Further, it is useful to compare portfolios and unit trusts on the basis of risk-adjusted returns. We
have already explained the co-efficient of variation which is equal to an investment’s standard
deviation divided by its mean return. We will now explain a few other risk adjusted measures
often used by fund managers to evaluate performance relative to risk.
Treynor ratio
This ratio measures the excess return per unit of systematic (unavoidable) risk as indicated
by a portfolio’s beta.
Treynor ratio = (average return of portfolio – average risk-free rate)/Beta of
portfolio
The Treynor ratio is particularly useful to compare unit trusts that may invest in similar sectors.
A fund with a higher Treynor ratio has achieved a higher return adjusted for market risk.
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Sharpe ratio (reward to variability ratio)
Whilst the Treynor ratio measures excess return per unit of systematic risk, the Sharpe
ratio measures excess return per unit of total risk as indicated by an investment’s standard
deviation.
Sharpe ratio = (average return of asset – average risk-free rate)/Standard Deviation
Auret and Vivian (see Table 3.9) conclude, on the basis of the Sharpe ratio, that bonds
offered a superior risk-adjusted return than equities over the period 1987 to 2010.
Sortino ratio
This is similar to the Sharpe ratio but this ratio only evaluates downside risk.
Sortino ratio = (average return of asset – minimum acceptable return)/downside
deviation
Downside deviation is the standard deviation of negative asset returns. This measure
assumes that investors are not as concerned with upside volatility and are mostly concerned
with downside risk. Rather than use the average risk-free rate, we can set a target return or
minimum acceptable return.
Jensen’s Alpha
Portfolio managers are often evaluated on their ability to generate positive Alpha. The
Capital Asset Pricing Model (CAPM), which we will cover in Chapter 4, is used to determine
a theoretical risk-adjusted required return.
Alpha = portfolio return – (risk-free rate + portfolio beta 3 (market return –
risk-free rate))
If a portfolio generates a return that is higher than its risk-adjusted required return, then
the portfolio manager will have generated positive Alpha. Essentially, the manager has
generated an excess return in relation to the risk-adjusted required return.
FROM THE REAL WORLD – UNIT TRUST FUNDS
The main objective of Coronation Fund Managers in introducing its Global Absolute Strategy
fund on 1 August 1999 was to achieve low risk and real returns. Since inception, Coronation has
achieved an average annual return of 15.7% per year up to 31 March 2018 with an annualised
standard deviation of only 7.7%. The fund’s latest 10-year return was 11.3% per year. Its lowest
monthly return was –4.5% and the maximum drawdown was –7.9%. The Sortino ratio was 2.0.
The fund was able to protect investors from significant drawdowns and market falls experienced
during the period June 2002 to April 2003 and during the global financial crisis period of
November 2007 to February 2009. Coronation states in its fact sheet:
The Coronation Global Absolute Strategy targets positive real returns with an overriding
focus on limiting downside returns or portfolio losses. Therefore, capital preservation in
real terms is equally important to return optimisation.
In order to achieve its investment objectives, the fund is able to invest in South African and
foreign equities, South African and foreign fixed interest securities, cash, South African and
foreign property, commodities and hedge funds.
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The Allan Gray Balanced Fund on 31 May 2018 had a fund size of R146.1 billion. This is a big
number. The fund factsheet states:
The Fund invests in a mix of shares, bonds, property, commodities and cash. The Fund
can invest a maximum of 30% offshore, with an additional 10% allowed for investments
in Africa outside South Africa. The maximum equity exposure is 75% and we may use
exchange-traded derivative contracts on stock market indices to reduce net equity
exposure from time to time.
Since inception on 1 October 1999, the fund has earned an annualised return of 16.9% per
year and its latest 10-year annualised return is 10.3% per year. The annualised monthly
standard deviation is only 8.9%. The maximum drawdown was 15.4%. Allan Gray has been
able to beat its market-based benchmark.
A low-cost way of getting access to the JSE is to invest in Index Funds such as the Satrix ALSI
Fund which is offered by the JSE and simply tracks the performance of the FTSE/JSE All Share
Index, thereby offering investors exposure to the 160 largest shares, but at a very low cost. The
annual return over the five years to 30 April 2018 was 10.63% per year. The Allan Gray Equity
Fund reported a return of 9.5% per year (after fees) over the latest five years to 31 May 2018
and the Coronation Equity Fund reported a return of 8.3% (after fees) for the latest five years to
31 May 2018. The Coronation and Allan Gray Equity Funds include direct exposure to foreign
equities which is not so for the SATRIX ALSI fund. Although the Coronation Equity fund did not
outperform its benchmark over the latest five years to May 2018, it did significantly outperform
(after fees) its benchmark since inception by 2.8% per year.
What returns did Warren Buffett achieve with Berkshire Hathaway?
Warren Buffett has been called the greatest investor in history. An investment of $100 in his
company, Berkshire Hathaway, in 1964, would have grown to $2 404 748 by the beginning of
2018. An investment of $100 in the S&P500 index (which reflects the largest 500 listed firms
in the USA) would have grown to $15 508 over the same period. What return did Buffett
achieve relative to the S&P500 over the period?
The compound annual return of Berkshire Hathaway was 20.9% from 1965 to 2017 as
compared to 9.9% for the S&P500. This represents a difference of 11% per year over 54
years. Yet, this does not tell the full story. There are dramatic kinks in performance over the
years. This is set out in Table 3.13.
Table 3.13 Berkshire Hathaway and S&P500 returns
In the period 1965 to 1991, Buffett’s compound annual return was 27.67% per year as
compared to 10.36% for the S&P500, an outperformance of 17.31% per year! However,
for the period 1992 to 2017, his compound annual return was 4.38% per year higher than
the S&P500. If we just focus on the period from 2001 to 2017, we see that he outperformed
the S&P500 by only 1.25% per year. Why is this? As Buffett has accumulated capital, it has
become increasingly hard to find investments that outperform the S&P500 by a significant
amount. Buffett stated that “a fat wallet is the enemy of superior performance” and
Berkshire has significant funds under management.
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Figure 3.17 sets out the annual returns of Berkshire Hathaway and the S&P500. As we can
see, Buffett’s outperformance occurred mainly in the years 1966 to 1994.
Figure 3.17 Berkshire Hathaway and S&P500 annual returns: 1965–2017
Berkshire Hathaway has also indicated higher volatility of returns but this volatility relates
mainly to dramatic upside movements in seven years over this period. This indicates one of
the limitations of employing volatility to measure risk. Downside movements were relatively
limited in relation to the S&P500 except for 1974. After 2002, performance was more closely
aligned to the S&P500, as was volatility. Berkshire Hathaway is a conglomerate with interests
in insurance, energy/utilities, railroads, industrial manufacturing, consumer products,
banking, and investments in companies such as Apple, Coca Cola, Bank of America, and
Wells Fargo. Will Buffett be able to offer returns significantly above the S&P500 in the
future? We think that outperformance of more than 2–3% is unlikely. But over a long period
of time, even one percent difference can make a large difference in the value of a portfolio.
The price of Berkshire Hathaway in early June 2018 was $294 055 per share!
SUMMARY
All investment decisions necessitate consideration of the required return, the expected
return, and the estimated risk. The risk to which a company is exposed can be classified into
two distinct categories. Firstly, there is business risk, measured by the degree of operating
leverage. Secondly, there is financial risk for a firm which has introduced fixed-interest debt
into its capital structure. Financial risk is measured by the degree of financial leverage. The
total risk is a product of these two categories and is expressed by the degree of combined
leverage.
For the investor, a statistical technique is used for expressing the risk of an investment as the
variation of expected returns, quantified in the form of the standard deviation of expected returns.
As a result, two fundamental parameters in financial management, namely the expected return
and the risk of an investment, can be captured in two summary statistics, the arithmetic mean and
the standard deviation.
These summary statistics may be used to gain greater insight into the probabilities of expected
outcomes. In order to make such interpretations, a normal distribution of expected returns is
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assumed and the properties of such distributions are used for further analysis. The co-efficient
of variation and the z scores enable comparison to be made between two individual shares with
differing expected returns and risk profiles.
An analysis of equity returns and bond returns indicates that investors do earn higher
returns for taking on the higher risks of investing in equities. Risk adjusted measures of
performance can be used to compare and rank the risk adjusted performance of funds.
The foundation has now been laid for further consideration of risk and return in the context
of a portfolio of shares. This chapter has been somewhat simplistic in assuming that the risk and
return information about individual shares is relevant for deciding between individual shares.
The next chapter provides the rationale for holding a portfolio of shares and further develops
the concepts discussed in this chapter.
APPENDIX 3.1 A BEHAVIOURAL FINANCE PERSPECTIVE ON RISK AND RETURN
The big money is not in the buying and the selling…but in the waiting. Charlie Munger. Buy right and
hold tight. John Bogle. No wise pilot, no matter how great his talent and experience, fails to use a
checklist. Charlie Munger. The most important quality for an investor is temperament, not intellect.
Warren Buffett.
In this chapter we have analysed market risk and return and we have demonstrated that although
equities involved higher risks, over time equity markets have offered significantly higher returns.
What about individual investors? What were their returns like? In this section we wish to analyse
how behavioural finance10 may explain investing behaviour. We reveal that our human traits and
biases may increase the risk of investing in equities beyond what is indicated by market volatility.
It seems that the risk of markets is compounded by the frailties of being human.
The evidence is that individual investors underperform a market index such as the ALSI or
the S&P500. Barber and Odean (2000)11 found that the average individual investor lost 3.7%
per year on a risk-adjusted basis. This finding is supported by the results from later studies.
The financial markets research firm, DALPER, reported underperformance of about 2% per
year for the 20 years to 2017. Morningstar reports lower underperformance in more recent
years, although in the last five years to June 2018 we have had a rising market and low volatility.
The performance of individual investors is important because increasingly in terms of defined
contribution retirement plans, investors are responsible for the investment decisions of their
retirement funds. Why do individual investors underperform the market index? The main
reasons are:
■■ Overtrading of shares resulting in high transaction costs
■■ Selling winning shares and holding onto losing shares
■■ A high concentration in a few shares resulting in undiversified portfolios
■■ Investing in the investor’s employer’s shares, and local companies rather than investing
internationally in order to achieve diversification
■■ Investing in shares on the basis of recent past performance
■■ Buying into bull markets and selling into bear markets and trying to time the market
■■ Over optimism that a rising trend in prices will continue or alternatively displaying a high
level of pessimism when market prices are falling
■■ Investors’ buying or selling decisions are often overly influenced by favourable or
unfavourable media attention
■■ An inability to differentiate a great company from a great investment. This is called
representativeness bias. The current share price may already be reflecting the fact that a
We set out an overview of behavioural finance in Chapter 1 in Appendix 1.1. The definitions of biases
referred to in this section are set out in Chapter 1 Appendix 1.1.
11
Barber, B.M. and Odean, T. (2000), Trading is hazardous to your wealth: The Common Stock Investment
Performance of Individual Investors, Journal of Finance, 55, 773–806.
10
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company has an outstanding management team, great products and is reporting excellent
financial results
The application of mental accounting to funds may lead to irrational decisions in respect
to risk and return decisions as well as portfolio construction
Overconfidence that the investor is able to accurately forecast future prices, cash flows,
dividends and/or earnings of companies
The conservatism bias may lead investors to under-react to changes in earnings and
prospects and then later over-react to further revisions
Herding and following the crowd is fraught with danger particularly during asset bubbles.
Sir Isaac Newton, one of the most brilliant minds in history, lost his wealth in the collapse
of the South Sea Bubble and wrote: I can calculate the motion of heavenly bodies, but not
the madness of people. Warren Buffett writes that one should be greedy when others are
fearful and be fearful when others are greedy.
There is another issue that is not captured above. Individuals tend to be underinvested in equities
and over the long term this will place their portfolios and perhaps even their retirement at risk. In
terms of prospect theory, investors are more sensitive to losses than gains. Investors will require a
50% chance of a gain of about R2 500 in order to offset a 50% chance of a R1 000 loss. This is also
called loss aversion which implies that investors are averse to locking in losses. This may imply that
the required premium for investing in equities above bonds or cash may be too high. Individuals
may be reluctant to invest in equities as this will probably mean incurring short-term losses if
investors monitor investments continuously. Fund managers often focus on “capital preservation”
as a key component of their investment fund’s investing strategy as this aligns with what individual
investors value.
Studies indicate that following and buying into the trend in prices may offer short-term
returns for individual investors but in the longer term, there is mean-reversion as share prices
on average tend to reverse after four years.
In terms of the disposition effect, investors are more likely to sell shares that have gone up
in price (“winners”) and are more likely not to sell shares that have fallen below cost, (“losers”).
If an investor buys a share for R100 and it falls to R70, then the investor is likely to hold on
hoping that the share price will recover so that he or she can at least break-even. If the share
rises from R100 to R130, then the investor is more likely to sell in order to lock in a gain.
These actions may not be rational and evidence indicates that investors that hold losers and
sell winners will lose on average. There is a saying that one should “cut your losses and let your
winners run” at least for a few years. It is also not tax efficient as the investor owes capital
gains tax on any realised gain.
Investors may be overconfident about their abilities to select winning shares. This
overconfidence bias may lead to a concentrated portfolio which increases risks due to a lack
of diversification. Overconfidence in the ability to pick shares means that an investor may
determine that diversification is not necessary. It may also mean that the investor becomes
emotionally attached to particular companies which makes it hard to sell a particular share.
Overconfidence may lead to too much trading and lower returns. Investors may invest in
shares that are most familiar (in terms of the familiarity bias and home bias) and this may limit
the performance of their portfolios and result in undiversified portfolios. Applying a
representativeness heuristic (shortcut) may mean, for example, that after a few years of high
earnings growth, investors will assume that this will continue indefinitely and be prepared to
overpay for such companies. This is particularly true for companies in cyclical sectors.
The Barber and Odean (2000) study found that whilst individual investors on average
earned 3.7% per year less than risk adjusted market returns, the 20% most active investors
earned about 10% less per year.
So how can individual investors significantly improve performance?
■■ Invest in ordinary shares for the long term and ensure that you have a 50–75% weighting
in equities in your portfolio
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Do not monitor your portfolio daily as this may lead to regret and loss aversion decisions
that are not in an investor’s best interests
Minimise trading to reduce transaction costs which are a drag on performance
Do not sell the winners and retain the losers. Value each share at each price point in
relation to future cash flows in order to reach buy or sell decisions
Follow a disciplined investment strategy. Use an investment checklist in order to avoid
impulse buying and selling
Increase the number of shares to at least 15–20 shares in a portfolio in order to achieve
diversification and avoid a home bias by investing in local and international companies.
Do not simply apply a naïve 1/n “diversification” strategy to asset allocation. If there are
five available funds, then investors are inclined to invest 20% of their savings in each
fund. This also means that you do not simply place 50% in equities and 50% in bonds.
Asset allocation requires a deeper analysis of markets, instruments and risk
On retirement, it is suggested that a retiree’s asset allocation should be weighted towards
low risk assets such as bonds. We consider this to be too simplistic when life expectancy
for a retiree and the retiree’s spouse may be another 25–30 years after retirement
Reduce costs by investing in a low-cost index fund. Alternatively, invest in a unit trust
fund if the fund has been able to outperform the index after fees over the long term
Do not try and time the market. Historically, it has been best to remain invested rather
than to try and time the market
Take action. Do not let inertia stop you investing. Implement an investment strategy.
Once you have invested in a diversified low-cost index, then inertia can be a positive force
as compared to excessive trading. Automatic rebalancing will ensure that the portfolio
retains its risk/return profile over time
Be conscious of all biases such as overconfidence, conservatism, representativeness,
anchoring and loss aversion as these can lead to a lack of diversification, overtrading,
biased valuations and lack of stringent analysis and due diligence
Avoid a narrow framing of investment decisions. A portfolio may be structured in a
particular way to achieve diversification. If one sector experiences losses and values fall,
then it is important to understand the hedging effects of such losses. For example,
investing in exporting companies may result in losses if the Rand appreciates but the
hedging objective remains valid and the local companies will perform strongly to offset
these losses. Do not focus only on the losses in one section of your portfolio. We should
evaluate portfolio performance in terms of its risk and return parameters rather than
focus on the gains and losses of the individual shares that make up such a portfolio.
It is important to note also that traits such as inertia and procrastination have saved many
investors, as well as cost them dearly. The saying, fools rush in where angels fear to tread is
pertinent here. However, Howard Marks when referring to bull markets, states that what the wise
man does at the beginning, the fool does at the end. Slow deep analysis is different though and you
may lose an opportunity but that is the price of caution. Overconfidence may project a sense of
purpose and knowledge which can motivate others. Imagine listening to your doctor ponder and
express doubts over your diagnosis12. However, confidence grounded on research and hard work
is more valued than bluster.
Richards and Willows (2018) have studied the characteristics of investors that engage in
frequent trading13. Dr Gizelle Willows has also studied the impact that gender and age have on
investment performance in South Africa. It seems that women do better than men.
Studies have found whilst doctors were very confident of their diagnoses whilst patients were alive, it was
found that up to 40% of such diagnoses were wrong when these patients were subject to autopsies after death.
It gets worse. Dr Michael Greger in his book, How not to die, lists medical care as the third leading cause of
death in the USA.
13
Richards, D.W. and Willows, G.D. (2018), Who trades profusely? The characteristics of individual investors
who trade frequently. Global Finance Journal, 35, 1–11.
12
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In Chapter 2, we found that not allocating a sufficient proportion of your portfolio to equities
would endanger the longevity of your pension. Although equities implied higher volatility, not
investing 50–75% in equities would mean that you would outlast your assets and end your days
in financial hardship. It seems like the biggest risk you can take is not taking a risk.
APPENDIX 3.2 COMPOUND ANNUAL RETURNS, ARITHMETIC AVERAGES AND
TOTAL SHAREHOLDER RETURNS
In this chapter we have determined the arithmetic average of an investment’s returns and have
computed the standard deviation to reflect the associated volatility and risk of an investment.
The arithmetic average is simply summing the returns or values and dividing by the number of
returns or values to determine an average. We have also used the compound annual growth rate
(geometric average) to explain market returns. In this section we will explore arithmetic and
geometric averages in greater detail before analysing the determination of total shareholder
returns.
We will use an example, GEM Ltd, from Year 1 to Year 7 whereby the share price has risen
with some volatility from R100 to R187. The compound annual growth rate is 11% (0.10996)
per year.
In Table 3.14, we have set out the workings of the above example in relation to the arithmetic
average as well as the standard deviation of the returns. We have computed the compound
annual growth rate (geometric mean) in three different ways and have set out the relevant Excel
functions such as the =GEOMEAN function, which we apply to the range of 1+return numbers.
Whilst Excel has a standard deviation function, we need to use logarithms in order to determine
the geometric standard deviation factor which we apply to the geometric return factor
(1+geometric return).
Table 3.14 Arithmetic means, geometric means and standard deviations
The arithmetic average of 15.6097% for GEM’s returns is higher than the compound annual
return (geometric mean) of 10.9959%.
The arithmetic mean will always be higher than the compound average growth rate
(geometric mean) unless there is no volatility. As volatility increases, then the arithmetic
mean will increase relative to the geometric mean.
Let’s take another example and assume that the share price of HBL Ltd which was initially
R100 goes up by 100% in Year 1 and falls by 50% in Year 2. The arithmetic average return is
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25% [(100% + (–50%))/2]. The compound annual growth rate is 0%. In Year 1, the value
went up by 100% to R200 and then fell by 50% back to R100.
When is the arithmetic mean relevant in this case? Well, if one was taking any gains off the
table and putting back any losses, then the average return of 25% would be relevant as the
opening investment in Year 2 would be R100 and then you lose R50, so that at the end of the
day you put back R50 to get back to your initial investment and you still have a R50 gain which
represents an average return of 25%.
The arithmetic average return will always be higher than the geometric average return due
to the asymmetry of returns. For example, if the share price of R100 falls by 20% in the first
year and then rises by 20% in the second year, this will result in an arithmetic average of 0%,
implying break-even and yet we would have lost money [R100 × (1–0.20) × (1.20) = R96].
The return in the second year will need to be higher in order to break-even. Due to the fall by
20%, we now have a base of R80 and therefore will need to achieve a return of 25% to achieve
break-even [R100 × (1 – 0.20) × (1.25) = R100]. The compound annual return is
(R100/R100)1/2 – 1 = 0%. The arithmetic average needs to be 2.5% per year, in order to
achieve the same result [(–0.20 +0.25)/2].
Outliers and volatility will tend to increase the arithmetic mean relative to a geometric
mean and is less likely to reflect the data. Assume data points of R100, R90, R500 and R110.
The average is R200 which is nowhere near most of the data points due to the outlier of R500.
It is also important not to let the tail wag the dog. Greater volatility may result in a higher
arithmetic average without affecting compound annual returns. For example, the only
difference between Company X and Y in Table 3.15 is that Company Y’s price jumped in Year
2 and therefore its returns reflect greater volatility and variability than Company X. We are
assuming zero dividends. We need to be cautious when comparing Company X to Company
Y, that we do not conclude in this case that Company Y offers a higher average return because
it is more volatile. In fact, it is because of its greater volatility, that the average return is
higher. On a compound annual return basis there is no difference between Company X and Y.
Table 3.15 Volatility and average returns
In general, when we are comparing companies over a long period, then arithmetic averages and
compound annual returns will tend to be aligned with volatility and higher arithmetic average
returns and compound annual returns will tend to reflect higher risk in the form of higher
volatility. We see that this reflects the returns in the real world based on our analysis of historical
financial returns in this chapter.
When we are analysing a long series of market data, then arithmetic averages can be useful
but we need to be aware of the impact that volatility may have on arithmetic averages. Warren
Buffett in our example reported a compounded annual return (geometric mean) of 20.9% as
compared to 9.9% for the S&P500. If we calculate Buffett’s arithmetic average return, then
this is 25.43% as compared to 11.39% for the S&P500.
Geometric means (compound average growth rates) may also be significantly affected by
beginning points and end points. If you can select your beginning and your ending, then this
will affect your geometric mean (compound annual return). So, whilst arithmetic means are
less accurate depending what happens in the middle of the data, geometric means can be
affected by beginnings and endings.
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We will assume that you are a fund manager and you need to report on your investment
over a number of years. The index values and annual returns of your investment fund over the
last six years is indicated below:
In terms of reflecting performance truthfully, your fund has achieved a compound annual return
of 6.1% per year [(143/100)1/6 – 1]. This does not look that good. So, instead of reporting the
performance of the fund over the prior six years, you select the beginning to be the end of Year
1, so that your return almost doubles to 12.3% per year [(143/80)1/5 – 1]. Of course, you can
bolster your return further by reporting the arithmetic average of 16.0% over the five years from
Year 2 to Year 6. These are all truths but may distort perceptions about future returns. In terms
of framing returns, these may also be gross returns before fees which will reduce compound and
average net returns. So, it is also relevant to watch how fees can affect net returns.
Total shareholder return
It is important to evaluate returns over time by considering the reinvestment of dividends.
Returns are not only beholden to changes in prices but also to dividend distributions. Let’s
compare investing in XYZ Ltd and ABC Ltd over the last six years. Table 3.16 depicts the share
price of either company over this period of time.
Table 3.16 Share prices, annual returns and compound returns
On the basis of price movements, XYZ has provided a compound annual return of 8.15% whilst
ABC has only provided a compound annual return of 6.39% per year. However, ABC has been
paying an annual dividend of R6 per share each year in Years 1, 2, 3 and 5 and paid a special
dividend of R10 in Year 4. No dividend was paid in Year 6. How does this change our analysis of
the relative performance of these two companies? It is important to compare not only price
returns but total shareholder returns which includes the reinvestment of dividends.
In Table 3.17, we have recalculated the compound annual return of investing in ABC Ltd
if a shareholder reinvests each dividend payable at the end of each year back into the company.
At the end of Year 1, we use the R6.00 dividend to purchase 0.0857 (R6/R70) of one share. At
the end of Year 2, we use the R6.00 to purchase 0.05 (R6/R120) of one share. By Year 6, the
reinvestment of the dividends will result in an investor holding on to 1.3233 shares by investing
the dividends in shares so that the value of one share at a price of R100 will have grown to
R191.87 (1.3233 × R145)
Table 3.17 Total shareholder return with the reinvestment of dividends
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The total compound annual return of investing in ABC Ltd, when one considers the reinvestment
of dividends is 11.47%. This is much higher than the return for XYZ which has not paid a
dividend. Therefore, consider the reinvestment of dividends when computing a total shareholder
compound annual return.
Does this make a significant difference to equity returns over time in South Africa? It sure
does. In fact, the difference is profound. Investing R100 in 1970, would have grown to R197 584
by 31 March 2018 if one had reinvested one’s dividends. Without reinvestment, the cumulative
value would be R27 737. Whilst this remains a good outcome, it is some way off the cumulative
amount if an investor had reinvested all dividends.
The compound annual return from reinvesting dividends since 1970 has been 15.9% per
year and 11.7% without the reinvestment of dividends. Why this is important, is that JSE
returns will often disclose the total shareholder return (TSI) and you should not expect the
compound annual return of the ALSI in the form of the TSI if you are spending your dividend.
Be more modest in your expectations but if possible, also endeavour to reinvest your dividends
as the power of compounding will lead to significantly higher returns over time. Dividends are
much more important to equity returns than most people think. So be wise with dividends.
Also, consider the impact of fees on your returns. On average most actively, managed unit
trusts or funds have not been able to outperform, after fees, the market index such as the
ALSI or the S&P500 index in the USA. Whilst the current inflows may create long-term
challenges, for now the momentum is with passive low-cost index fund investing. Even hedge
funds have not been able to beat the market, after fees and I refer you to Berkshire Hathaway’s
annual report in which Warren Buffett reports on his bet against hedge fund performance in
favour of a low-cost index fund investing strategy.
In this section, we have offered some insights into reporting on performance in the form
of geometric averages (compound annual returns) and arithmetic averages. We have also
reflected on the impact of the reinvestment of dividends on compound annual returns in
specific examples and for the JSE.
S
SELF-STUDY PROBLEM
The following limited information is available for returns on two shares listed on the Stock
Exchange.
Despite the limited number of readings, a normal distribution of returns may be assumed.
In addition, past performance is considered to reflect expected future performance.
Required:
(a)Calculate the average return, standard deviation, and co-efficient of variation for each
of the two shares.
(b)Using the properties of a normal distribution and the z score tables, establish the
probability for each share of a return lower than 10%.
(c)Taking the role of an investment adviser, recommend one of the two shares to a client
who wishes to make a choice between an investment in Gipley Ltd or an investment in
Petros Ltd. Advise the client of some of the issues which should be considered.
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Suggested solution
(a)
(b) Return lower than 10%
(c) All investment choices depend on the individual investor’s propensity for risk. It is
apparent that Gipley is a more volatile share than Petros. Because of this characteristic,
investors require a higher expected return than they do for an investment in Petros. This
is evidenced from the higher return which has been achieved in the past.
Based on the analysis, there is still a lower probability of achieving a return of less than
10% by buying the shares of Gipley rather than Petros. However, investors who are
very risk averse may consider even such a risk to be unacceptable. It can be calculated
that the probability of suffering a negative return from an investment is around 0.5%
or one chance in 200, while there is virtually no chance at all, based on probabilities, of
suffering a negative return from an investment in Petros.
The most significant issues, once probabilities based on past performance have
been discussed, relate to future expectations. We are not told, for example whether
these companies are both listed in the same sector. Industry factors and the investor’s
expectations regarding the future would be considered.
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Q
QUESTIONS
Question 3.1
A dictionary defines risk as “the chance of bad consequences”, and uncertainty as “not to be
depended on”.
Required:
(a) Discuss these terms in the context of financial management.
(b) Identify the relationship between estimated risk and expected return, with respect to a
financial investment.
(c) Explain why an investment in a government security may be considered to be a riskless
investment.
Question 3.2
When you take a risk you should be rewarded with a return. Why is this nexus the cornerstone
of finance?
Question 3.3
Different financial instruments have different inherent risks. Describe the risks associated with
the following:
1. Government bonds
5. Preference shares
2. Corporate bonds
6. Convertible notes
3. Debentures
7. Convertible Preference shares
4. Ordinary shares
Question 3.4
When assessing the overall risk of a company, financial managers take cognizance of business
risk and financial risk.
Required:
(a) Define business risk and discuss the method by which it may be measured.
(b) Define financial risk and discuss the method by which it may be measured.
(c) Discuss the actions a financial manager may take to reduce the overall risk of the company
and the effects this may have on shareholders.
Question 3.5
The following information is available for Astrid Ltd and Duncast Ltd:
Required:
(a) Find the break-even point for each company in units.
(b) Calculate the degree of operating leverage for each company at 25 000 units.
(c) Explain the differences that you observe between these companies’ break-even points and
degrees of operating leverage.
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Question 3.6
The income statement of Flexet Ltd for the past year is as follows:
Required:
(a) Calculate the degree of operating leverage.
(b) Calculate the degree of financial leverage.
(c) Calculate the degree of combined leverage.
(d) Find the break-even point in units.
Question 3.7
The following are abbreviated contribution income statements of two companies, both of which
are active in the food and beverage industry.
Required:
(a) Calculate the degree of operating leverage.
(b) Calculate the degree of financial leverage.
(c) Calculate the degree of combined leverage.
(d) Find the break-even point in rands.
(e) Discuss the relative riskiness of the two companies based on the leverage factors calculated.
Question 3.8
An investor purchased 500 shares in Glicks Stores Limited at the beginning of its financial year at
R22.50 per share, paying 3% brokerage costs. The book value per share on that date was R10.60.
During the course of the year, the company paid a dividend of R2.40. One year later, the company
reported earnings per share of 470 cents. On that date the book value per share was reported as
R13.80. The investor sold the shares for R30.70 each, paying 3% brokerage on the transaction.
Required:
(a) Calculate the return which the shareholder earned for her investment in Glicks stores Ltd.
(b) Discuss the difference between return on equity, return on investment, and the return to the
shareholder.
(c) If the investor had decided not to sell the shares at the end of the year, calculate her return.
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(d) Comment on the riskiness of the investment in Glicks Stores Ltd based on the information
provided.
(e) If the period had been eight months rather than one year, all other information remaining
the same, calculate the return to the shareholder.
Question 3.9
You wish to purchase shares in two companies of the following six that are available:
■■ Company A with an expected return of 10% with a standard deviation of 10%
■■ Company B with an expected return of 10% with a standard deviation of 15%
■■ Company C with an expected return of 15% with a standard deviation of 15%
■■ Company D with an expected return of 10% with a standard deviation of 20%
■■ Company E with an expected return of 15% with a standard deviation of 20%
■■ Company F with an expected return of 20% with a standard deviation of 20%
Required:
(a) Plot these shares on a risk/return graph such as indicated below.
20
15
Return
%
10
5
5
10
15
20
Risk (Standard Deviation)
%
(b)As an investor who is willing to take risks in the hope of retiring early, which two shares
would you buy? Explain.
(c)As a cautious investor who requires a steady return on your investments, which two shares
would you buy? Explain.
(d)Investors are said to be risk averse. Does this mean they will not invest in risky assets?
(e)Why are government bonds considered low risk when there is always the chance that
interest rates will change and the value of the bond will change accordingly?
Question 3.10
Lighthouse Ltd is considering investing in a project that may offer the following possible rates of
returns. The probability distribution of returns from the project is set out below:
What is the expected return from the project? What is the standard deviation of returns?
Question 3.11
Emma Dlamini is considering two investments and can only invest in either the shares of Company
X or in the shares of Company Y. The following information regarding returns and probability
distributions of returns is relevant:
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Required:
(a) What is the expected return of X and Y?
(b) Calculate the standard deviations of X and Y’s returns
(c) What is the co-efficient of variation?
(d) What would you recommend? Why?
(e)Instead of Share Y offering a probability of 20% of achieving a 30% return, assume instead
that the possible return is 40%. How would this affect the investment decision?
Question 3.12
Home Wares Ltd is a listed company which provides home solutions. The company has benefited
indirectly from the growth in residential developments. As an investor in the shares of the
company, you wish to determine how the company’s shares have performed in relation to the
market. You would like to also understand the relative risk of investing in the company as
compared to the market. The following information on returns for Home Wares and the market
is relevant:
Determine the average return for the company and the market. What is the standard deviation
for the company and the market? Comment on the results.
Question 3.13
Based on various scenario planning and economic forecasts, the probability of various states
of the economy have been determined by an economic analyst. The various possible states of
the economy depend upon factors such as the national debt, foreign investment prospects and
internal political factors. The financial manager of Plus-Two Ltd, manufacturers of fashion
wear for teenagers, have predicted the most likely return to shareholders given the state of the
economy as follows:
Conditional state of the economy
Boom
Probability of
state of economy
Expected
return
5%
40%
Strong economy
15%
20%
Moderate economy
60%
10%
Recession
15%
0%
5%
–10%
Deep recession
Required:
(All calculations may be rounded to two decimal places of a percentage.)
(a) Calculate the expected return.
(b) Calculate the variance of the expected return.
(c) Calculate the standard deviation of the expected return.
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(d) Assuming a normal distribution of returns, calculate the probability that shareholders will
receive a return in excess of 25%.
Question 3.14
Environ Ltd has gathered the following information regarding the probable costs of two alternative
projects designed to recycle effluent which is environmentally sensitive. One of the projects must
be accepted in accordance with legislation relating to environmental pollution. The possible net
cash flows have all been discounted at 16%, but are heavily dependent upon factors that cannot
be predicted with certainty. However, probabilities of occurrence have been established.
Required:
(a) Calculate the expected present value (or cost) of each of the two projects.
(b) Using mean-variance analysis, and the assumption of continuous probabilities, recommend
which project should be accepted.
(c) Discuss the issues that will require consideration depending upon whether the probabilities
are discrete probabilities or a continuous probability distribution.
Question 3.15
Siyabonga Ltd is attempting to measure the riskiness of two projects which have the following
cash flows in different, equally likely, states of the economy.
Required:
(a) Establish, using the standard deviation of cash flows as a measure of risk, which project is
riskier.
(b) Establish, using the co-efficient of variation of cash flows as a measure of risk, which project
is riskier.
(c) Explain which measure of risk you would prefer.
Question 3.16
Baxter Ltd is faced with a problem of fluctuating costs of materials which differ, dependent upon
the type of machine which is used. Two different machines, each producing the same product,
are available. Various possible fluctuations from the estimates have been established for each
machine. The resultant table of possible costs and probabilities assigned to those costs is as
follows:
Binding machine
Flexing machine
Probability
Costs
Probability
Costs
%
R000
%
R000
10%
40%
30%
20%
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750
900
1,420
1,500
20%
30%
50%
1,050
1,400
1,300
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3-49
Required:
(a) Determine the most likely cost for each machine, assuming:
(i) that the probabilities are discrete;
(ii)that the probabilities reflect point estimates on a continuous distribution which closely
approximates a normal distribution.
(b) For each machine, determine the probability that the cost will be in excess of R1.2 million,
using the properties of a normal distribution and z scores.
Question 3.17
The past returns on an investment in the shares of Nwabisa Ltd have been recorded and processed
to produce the following statistical indicators:
Mean return
24%
Standard deviation
9%
You may assume that the distribution around the mean has the properties of a normal
distribution.
Required:
(a) State the most likely return which an investor may expect to receive from an investment in
the shares of Nwabisa Ltd.
(b) Discuss the issues which should be considered in establishing the likelihood of the return
being different to the expected return.
(c) Using z scores, establish the probability of the following outcomes:
(i) a return of more than 33%
(ii) a return of less than 10%
(iii) a negative return.
Question 3.18
The following summary statistics are generated for the investment listed below.
Mean return
Standard
deviation
Government bonds
8%
2%
Paveco Ltd
14%
8%
Energet Ltd
18%
12%
Argyle Ltd
20%
11%
You may assume that the distribution around the mean has the properties of a normal
distribution.
Required:
(a) Provide reasons (if such reasons exist) as to why an investment in a government bond may
have a standard deviation other than zero.
(b) Calculate the co-efficient of variation for each of the three shares.
(c) Assume an investor is considering purchasing one of the above four shares. Identify
considerations which should be taken into account and make a recommendation, if possible.
(d) Identify an incongruity which exists between the summary statistics of Energet and Argyle
and discuss whether such summary statistics are feasible.
(e) Calculate the probability of the return on investment in the shares of Paveco being negative.
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Question 3.19
As a financial planner you are called upon to advise your clients on the shares they should invest
in. The choices are:
(a)
Mr Fossil who is risk averse wants you to rank the shares in the order he should consider
investing in them.
(b) Mr Steady is risk neutral and also seeks the appropriate order of investments in which he
should invest.
(c) Mr Quickbuck is a risk taker who wants to retire early in life. Suggest the appropriate order
of the above investments that will satisfy his risk profile.
Question 3.20
The following returns have been obtained from the company’s respective financial statements:
(a) Calculate the expected return and standard deviation of the above companies.
(b) An investor requires high returns but is indifferent as to the risk. Which company would he
invest in?
(c) You are a risk averse investor. Does your choice change?
Question 3.21
SQ Ltd is listed on the JSE and its share price at end of each year is set out as follows:
SQ paid no dividend in 20x1, but consistently paid a dividend of R8 per share at year end in each
year from 20x2 to 20x4. Prices are stated ex-dividend.
Required:
(a) Determine the arithmetic average annual return and compound annual return for the period
until 20x4, based on price movements only and ignoring dividends.
(b) What is the arithmetic average return including annual dividends?
(c) What is the total shareholder return (compound annual return) if dividends are reinvested
at the end of each year?
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4
DIVERSIFY TO REDUCE RISK
A unit trust represents the pooling of investors’ funds into a collective investment. Investment
managers such as Allan Gray, Old Mutual, Sanlam, and Coronation invest these funds in shares,
property, bonds and money market instruments. Unit trusts enable small investors to invest a small
amount of money and yet achieve effective diversification. According to Allan Gray, the benefit of
diversification is that risk is spread among investments that are uncorrelated.
Seema Dala of Allan Gray writes that the JSE “makes up just over 1% of the world’s total
listed equity universe by market capitalisation. … Intuitively it makes sense to increase exposure
to the sectors and markets that are underrepresented in our local market. Adding international
equity exposure diversifies your returns.” (Allan Gray Quarterly Commentary, Q1, 2013) Offshore
equity investing will improve diversification and enable South Africans to invest in companies
such as Amazon, Apple and Microsoft. South Africans will also be able to invest in sectors that are
poorly represented on the JSE such as information technology, healthcare, pharmaceuticals and
biotechnology. It is important to realise just how concentrated the JSE is, as five companies make
up about 50% of the JSE ALSI. One company, Naspers, makes up over 20% of the JSE ALSI.
Naspers’ major investment is Tencent, a Chinese internet-based technology and gaming company1.
Avoiding concentration and achieving a greater degree of diversification is a good reason to invest
offshore. Diversification also involves investing across asset classes such as shares, bonds and other
assets. The Allan Gray Balanced Fund states in its September 2018 fact sheet that “The Fund
invests in a mix of shares, bonds, property, commodities and cash”. The Fund will also invest up
to 30% offshore. In this chapter we will explore the concept of diversification and portfolio theory.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Explain the impact of diversification on the expected return and risk of a portfolio of
shares.
■■ Calculate the following indicators of risk and expected return on a portfolio of shares:
–– expected return on a two-asset portfolio;
–– risk of a two-asset portfolio using covariance;
–– expected return on a multi-share portfolio;
–– beta of a portfolio;
–– expected return on a leveraged portfolio;
–– standard deviation of a leveraged portfolio.
■■ Understand the concept of an efficient frontier.
■■ Apply the concept of the security market line.
■■ Evaluate the concept of market efficiency.
■■ Understand how Exchange Traded Funds (ETFs) work
■■ Explain how behavioural finance may influence portfolio decisions
■■ Use Excel to determine betas.
■■ Understand the use of betas in practice.
In fact, the market value of Naspers’ holding in Tencent in May 2018 was about 150% of Naspers’ market
capitalisation, which effectively means that the other assets owned by Naspers had a negative value! We refer to
this in Chapter 1 in Appendix 1.1 on the limits to arbitrage.
1
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INTRODUCTION
The old adage that you shouldn’t place all your eggs in one basket reveals a general approach
to risk. Because virtually all future outcomes are uncertain, it would not be wise for an
investor to place all available funds in one investment. At the time of investment, it is not
known with certainty which investments will succeed and which will fail. It is therefore sensible
to diversify into a number of investments in the expectation that those which are profitable
will at least compensate for the loss which may be sustained from those that are not. This is
the fundamental principle for adding a risk premium to the risk-free rate, for an individual
investment opportunity which is not risk-free, in order to arrive at the required return for
that investment. This principle was fully outlined in Chapter 3.
In this chapter we describe the effect on expected return and estimated risk of diversifying
– of investing in more than a single investment. We confine the discussion to investments on
securities markets, because the share prices are known at the time of purchase and there is a
past record of returns available which is useful for forecasting future returns. The principles
of portfolio management may, however, be generalised to encompass all assets in which an
investor may invest.
Using modern portfolio theory and the capital asset pricing model, it will be demonstrated
that holding a portfolio of shares will always be a superior investment strategy to selecting
an individual share. Portfolio management is based on the work of many researchers but
pioneered by Markowitz (1959) and Sharpe (1964). Portfolio theory is based on a number of
assumptions regarding the way in which investors and stock markets function. While these
assumptions may seem restrictive, the principles are fundamental to an understanding of
investment strategies and are essential to an understanding of financial principles.
It also implies that if investors can effectively diversify risk by investing in a portfolio of
assets such as shares, then a firm does not need to diversify its operating assets in order to
reduce the investment risk to its shareholders.
1 TWO-ASSET PORTFOLIO RISK AND RETURN
Holding more than one investment in financial assets is generally referred to as holding a
portfolio of investments (although there may be a one-asset portfolio). The principles used
when establishing the expected return of a portfolio will be discussed using a two-asset
portfolio and then by generalising the principles to a portfolio with many financial assets.
Example 4.1: Investing in a two-asset portfolio
An investor decides to invest R10 000 in a portfolio which may consist of any combination
of shares in Plasco Ltd and Quinco Ltd. The following summary expected return (Re) and
standard deviation () statistics are available for the two companies:
Plasco Re = 30%;  = 12.6% and Quinco Re = 20%;  = 10.3%
If, for example, R5 000 is invested in Plasco and R5 000 in Quinco, it would be expected that
the return on the portfolio would be a weighted average of the proportion invested in each.
This example will be used as a basis for establishing the measure of return and the measure
of risk for possible portfolio combinations.
Measuring two-asset portfolio returns
An investor who decides to diversify by buying shares in two companies will expect a return
dependent on the proportion of funds invested in each share. The expected return of the
portfolio will quite simply be the weighted average of the expected returns of the individual
shares as depicted in Table 4.1.
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4-3
Table 4.1 Expected returns for various portfolios of P and Q
It is clear from Table 4.1 that the greater the proportion of funds invested in P Ltd, the higher the
expected return becomes. The general formula for calculating the expected return of a portfolio
n
is:
Rp = ​​ ​​  Wi × Ri(Formula 4.1)

i=1
where: Rp = the expected return on the portfolio
Wi = the proportion of funds invested in share i
Ri = the expected return on share i
Expected return is not the only parameter on which to base the decision. A measure of risk
for the various portfolio combinations is required.
The principles of portfolio risk
The risk of a portfolio depends not only on the riskiness of the individual shares which
compose the portfolio, but also on the relationship between their returns. The tendency
may be to expect that portfolio risk is calculated in a similar fashion to portfolio return – i.e.
using a weighted average. However, this is not the correct procedure.
Assume we are able to collect the historical information on the share price performance
of the two shares P and Q, and they are as listed in Table 4.2.
Table 4.2 Past performance of shares P and Q, and an equally weighted portfolio PQ
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FINANCIAL MANAGEMENT
The following is apparent from the data collected and processed:
■■ Share P has an average return of 30% over the period, and share Q has an average
return of 20%.
■■ The standard deviation of returns has been calculated using Excel, and reflects the
greater variability of returns for share P, with a standard deviation of 12.6% compared
to 10.3% for share Q.
■■ Of particular relevance is the fact that the two shares tend to move in similar directions
in each year. In year 1, for example, both shares achieved well above the mean return,
whereas in year 2 both shares achieved well below their mean. This pattern is evident
throughout the 8-year period.
■■ The standard deviation of an equally weighted portfolio lies between those of each
individual share. Because the shares move in near-perfect unison, the risk of the
portfolio reflected in the standard deviation of 11.4% is very close to the weighted
average of the two standard deviations.
The results are reflected in Figure 4.1.
Figure 4.1 Returns on P and Q: near-perfect unison: 50/50 portfolio
The measure of harmony in movement between the two shares can be calculated in further
summary statistics. When only one share was under consideration we used the square root of
its variance, the standard deviation. For two shares we use the covariance, often expressed in
a standardised form as the correlation co-efficient. This statistic reflects the degree to which
two variables move together. The values of correlation lie between +1, which is perfect
positive correlation, and –1, which is perfect negative correlation. Note the correlation coefficient is a high positive figure of 0.978.
A correlation co-efficient of 0 indicates that there is no correlation between the two
variables. In this hypothetical example, where P and Q move in near-perfect unison, a state
of near-perfect positive correlation exists. This situation would seldom exist in practice.
Covariance and correlation are explained in greater detail in Chapter 3 and the data
set out in Table 4.1 for shares P and Q is used in Chapter 3 to define and determine the
covariance and correlation co-efficient. We apply the appropriate calculations, as well as use
Excel to determine covariance and correlation. Please refer to Chapter 3.
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4-5
Assume now that all the rates of return are identical to those in Table 4.2, but that the
timing is different. Notice from Table 4.3 that the average return and standard deviation for
each share remains identical, but the co-movement, reflected in the covariance statistic and
the correlation co-efficient, is significantly different.
Table 4.3 Past performance of shares P and Q, and an equally weighted portfolio PQ
If the data were as presented in Table 4.3:
■■ Share P has an average return of 30% over the period, and share Q has an average
return of 20%. This is identical to the previous case.
■■ The standard deviation of returns has been calculated using Excel (=STDEVP), and
reflects the greater variability of returns for share P, with a standard deviation of 12.6%
compared to 10.3% for share Q. This too is identical to the first case. Note that we have
determined the population standard deviation. We did not use the STDEV function,
which calculates the standard deviation for a sample2.
■■ The difference, however, is that the two shares move in opposite directions in each year.
In Year 1, for example, when P performs well above its mean return, Q performs well
below its mean return. This pattern is evident throughout the 8-year period.
■■ The result of this pattern of returns is that an equally weighted portfolio tends to
have very similar returns each year, thus there is much greater consistency, and less
variability, reflected in the very small standard deviation of the portfolio of only 1.9%.
■■ Of equal interest is the correlation co-efficient, which is very highly negative at minus 0.9667.
Later in the chapter, the manual calculation of these important summary statistics for a twoasset portfolio will be demonstrated. Figure 4.2 illustrates the movement of each share over
the 8-year period, and that of an equally weighted portfolio, based on the historical returns in
Table 4.3.
2
In order to be accurate, we should really divide by (n – 1) rather than n in our examples. See for example, Table
4.4 and the Self-study example at the end of the chapter in which we should divide the squared deviations by (5 – 1)
rather than by 5. In practice, we will be working with very large samples and so there will be very little difference
between the use of (n – 1) and n. So we have retained n to reflect the reality that the results will be very close in
practice whilst in our examples which have very limited observations, the effect will be significant. In Excel, use the
=STDEV function to reflect the standard deviation of a sample.
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Figure 4.2 Returns on P and Q: near-perfect negative correlation: 50/50 portfolio
The frequency distributions of returns on share P, share Q, and the portfolio of shares P and
Q respectively, are roughly graphed in Figure 4.3.
Figure 4.3 Frequency distribution of two individual shares and the portfolio of two shares
The following can be noted:
■■ The dispersion around the mean of Q Ltd is considerably tighter than the dispersion
around the mean of P Ltd. This is in accordance with the expectation that P Ltd is more
risky than Q Ltd, but offers a higher expected return.
■■ The dispersion around the mean of the portfolio of 50% P Ltd and 50% Q Ltd is tighter
than that of either P Ltd or Q Ltd. This means that the risk of the portfolio, in this case,
is lower than the risk of holding either P Ltd or Q Ltd individually.
Just as it is unlikely that two shares will be perfectly positively correlated, it is also unlikely
that two shares will be perfectly negatively correlated. Because of the many general factors
that are likely to influence all shares in a fairly similar manner at any given time, shares will
tend to be positively correlated rather than negatively correlated. In general, however, it can
be accepted that anything less than perfect positive correlation will cause the portfolio risk
to be lower than the weighted average of the standard deviations of the two shares held in
the portfolio.
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4-7
Measuring two-asset portfolio risk
The risk of a two-asset portfolio has been demonstrated in principle to depend upon the
extent to which returns move in harmony with each other. The extent of this co-movement
may be measured by calculating the covariance between two shares, denoted by covA,B, or its
normalised statistic, the correlation co-efficient, denoted as rA,B. Once these indicators have
been calculated, it is possible to derive the variance and standard deviation of the two-asset
portfolio. These procedures are best illustrated using an example.
Example 4.2: Statistical calculations for two-asset portfolio
Information is available for two shares – Benix Ltd, listed under the general retail sector, and
Genhold Ltd, listed under the media and entertainment sector. The returns for shareholders
have been calculated for the last five years.
Before proceeding with the statistical procedures illustrated in Table 4.4, the following must
be noted:
■■ The number of data points used is for illustrative purposes only. Five points are
inadequate for any meaningful statistical interpretation in practice.
■■ It is assumed that the distribution has the characteristics of a standard normal
distribution.
■■ Past performance is considered to be valid for the purpose of predicting future
expectations.
Table 4.4 provides the basis for calculating the mean and standard deviation for each share,
as well as the covariance and correlation co-efficient of the two shares.
Table 4.4 Calculation of the mean, standard deviation and covariance
From Table 4.4 the following should be noted:
■■ Columns one and two list the past returns to shareholders over the last five years. Each
column_ is totalled and divided by the numbers of readings (five) in order to obtain the
mean (​x​), which then serves as the expected return.
■■ Columns three and four reflect the deviations from the respective means. These are
squared in columns five and six. The columns are totalled and divided by the number of
readings (five) in order to obtain the variances (2) of 0.10% and 0.356%. The variances
may be converted to standard deviations () by finding their square roots.
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4-8
■■
■■
■■
FINANCIAL MANAGEMENT
Each deviation of Benix (db) in column three is multiplied by the deviations of Genhold
(dg) in column four, in order to obtain (db)(dg) in column seven. These are totalled
and divided by the number of readings (five) in order to obtain the covariance covbg of
– 0.026%.
Note that these two shares did not always move in harmony. For example, in year one, when
Benix achieved 2% above its mean performance of 24%, Genhold achieved 6% below
its mean performance of 30%. These contrary performances have resulted in a negative
covariance of –0.026%.
The covariance term may be normalised – i.e. expressed in a manner such that
all readings will fall between –1 and +1. Such normalised covariance is called the
correlation co-efficient and is calculated as follows:
covbg
bg = ​ 
​
(Formula 4.2)
b × g – 0.026%
= ​ 
​
3.16% × 5.97%
= – 0.14
where:
bg = correlation co-efficient of B and G
b = standard deviation of B
g = standard deviation of G
covbg = covariance of B and G
This summary statistic indicates that there is a slight negative correlation between Benix
and Genhold.
It also follows from Formula 4.2 that if both standard deviations are known, as well as
the correlation co-efficient, then the covariance may be calculated as follows, all notation
being identical to Formula 4.2
covbg = bg × b × g(Formula 4.3)
We now wish to measure the variance of a portfolio of shares comprising a proportion
of both Benix and Genhold shares. We will thus develop a variance matrix from which a
formula for calculating the variance and standard deviation of a portfolio may be derived.
Assume we wish to construct a portfolio of 25% Benix and 75% Genhold. The first step
in constructing a variance matrix requires that the relative weighting for each block in the
matrix be determined. This is illustrated in Table 4.5.
Table 4.5 Weights in a variance matrix. This requires that the relative weighting for each block in the matrix
be determined.
Benix (25%)
Genhold (75%)
Benix (25%)
0.0625
0.1875
Genhold (75%)
0.1875
0.5625
From Table 4.5, the following must be noted:
■■ The figures obtained in each block represent the weighting which each will have in the
total variance of the portfolio.
■■ The sum of the weightings is equal to one.
The relative variance and covariance figures may now be inserted. In Table 4.6, it is apparent,
for example, that the block matching Benix with Benix uses the variance of Benix, while the
block matching Benix with Genhold uses the covariance between Benix and Genhold.
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4-9
Table 4.6 Variance matrix for Benix and Genhold
Benix (25%)Genhold (75%)
Benix (25%)
0.0625 × 0.10%
0.1875 × –0.026%
Genhold (75%)
0.1875 × –0.026%
0.5625 × 0.356%
The sum of all the variances and covariances multiplied by their weightings in the matrix
equals 0.19675% (0.00625% + 0.20025% – 0.004875% – 0.004875%). This is the variance of
the portfolio comprising 25% Benix and 75% Genhold.
This method of arriving at the variances is cumbersome and may be expressed and
calculated by a formula which derives from the matrix as follows:
 2p​ ​= W​2b​ ​2b​+ W​2g ​ ​2g ​+ 2WbWg × covbg
(Formula 4.4)
where: ​2​= the variance of the portfolio
p
2
W​
​and W​2g ​= the weight (proportion) invested in B and G respectively
b
(note: Wb + Wg = 1)
​2b​ and ​2g ​= the variance of returns on shares B and G respectively
covbg = the covariance of the returns on the two shares
Applying Formula 4.4 to calculate the risk of a portfolio comprising 25% in Benix and 75%
in Genhold results in the following:
​2p​= (0.25)(0.25)(0.10%) + (0.75)(0.75)(0.356%) + (2)(0.25)(0.75)(–0.026%)
= 0.19675%

So p = ​ 0.19675% ​
= 4.44%
Note that Formula 4.4 can also be expressed using the correlation co-efficient, if the
covariance is not known, as follows (with notation identical to Formula 4.4). Refer back to
Formula 4.3 for a breakdown.
​2p​= W​2b​​2b​+ W​2g ​​2g ​+ 2WbWgbgbg(Formula 4.5)
Of course, you may not like Formulae 4.4 and 4.5. Well, in this example we can determine
the standard deviation of the portfolio in another way. Firstly, we will use Excel to determine
the weighted average return for each year by multiplying the return for each security by
its weighting in the portfolio to determine a weighted-average return for each year. For
example, we would determine the weighted-average return for Year 2 to be 31.3% [(0.25 ×
20%) + (0.75 × 35%)]. We then determine the average return and standard deviation of the
portfolio returns. In this case, we have used the Excel function [=STDEVP(B16..F16)] to
determine the standard deviation of 4.44%. This agrees with the result that we obtained by
using Formula 4.4 and is presented in Table 4.7.
Table 4.7 Portfolio return and portfolio standard deviation
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FINANCIAL MANAGEMENT
Example 4.3: Risk of two-asset portfolios
Share P has Re = 30%;  = 15% and share Q has Re = 20% and  = 10%. The correlation
co-efficient for the returns of the two companies is known to be +0.4. Determine the risk of
the portfolio for weights of p = 100%, 75%, 50%, 25% and 0%.
Only one calculation is shown as an example, where Wp = 25% (by default Wq must
be 75%), the others being tabulated in Table 4.8. Use Formula 4.5 to check the standard
deviations of the portfolio combinations (p) tabulated in Table 4.8. To solve for Rp refer
back to Formula 4.1:
​2p​= (0.0625)(0.0225) + (0.5625)(0.01) + 2(0.75)(0.25)(0.4)(0.15)(0.10)
= (0.001406) + (0.005625) + (0.002250)
= 0.009281

So p= ​ 0.009281 ​
= 0.096338 = 9.6%
Note that in this case the risk of the portfolio as measured by the standard deviation is lower
than the risk of Q Ltd. In other words, holding the portfolio is less risky than the lowest-risk
individual share. This is a special case and cannot be generalised. In all cases, however, the
portfolio risk measured by the portfolio standard deviation will be less than the weightedaverage standard deviations of the two shares. The full range of risk for holding different
proportions of the shares is as follows.
Table 4.8 Portfolio risk and return
% Invested in P Ltd
% Invested in Q Ltd
p
Rp
100%
0%
15.0%
30.0%
75%
25%
12.5%
27.5%
50%
50%
10.5%
25.0%
9.6%
22.5%
10.0%
20.0%
25%
0%
75%
100%
We are now in a position to graph the expected return and risk of portfolios comprising
different proportions of shares in P Ltd and Q Ltd. This is displayed in Figure 4.4.
Figure 4.4 Feasible set of portfolio of two assets
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4-11
The line ABC represents a feasible set of portfolios, that is, all the possible combinations
of P and Q are represented. It makes sense to hold a combination of P and Q which lies
between points A and B, because any portfolio between B and C would be inferior to a
portfolio between A and B. Point y, for example, is superior to point C because it results in
a higher return for the same degree of risk. These relationships were originally identified by
Markowitz, who gave the name efficient frontier to the line AB.
In Table 4.9, we have expanded Table 4.8 to include more portfolio weightings. We then
apply Formula 4.5, assuming a correlation (p) of 0.4 and the same returns and standard
deviations.
The resulting standard deviation and expected return is presented in Table 4.9. If the
weighting of P is 25%, we will note that the portfolio standard deviation is 9.6%, which is
what we calculated using Formula 4.5.
Table 4.9 Portfolio risk and return – expanded
We have then calculated the same tables assuming a correlation (p) of 1, –1 and 0. We can
plot this to see how correlation will affect portfolio risk as measured by its standard deviation.
The relationship between the portfolio return and risk for each level of correlation (p) is
depicted in Figure 4.5.
Figure 4.5 Portfolio risk and return for P & Q
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Perfect correlation (p = 1) results in a straight line from P to Q and so diversification does
not result in lower risk relative to return as the standard deviation is simply a weighted
average of the standard deviations of P and Q. If the correlation between the share returns
of P and Q are less than 1, then there will be some benefit from diversification. If P and Q
are perfectly negatively correlated (p = –1), then this will result in a significant reduction in
risk depending on the relative weightings of P and Q in the portfolio. A portfolio made up
of 40% of P and 60% of Q will result in a portfolio with zero risk, if the share returns are
perfectly negatively correlated (p = –1).
It is important to note that with diversification and less than perfect correlation, we get
a weighted-average rate of return but a less than weighted-average level of risk. We get
something for nothing.
Positioning an investor on the efficient frontier
Which combination of shares should an investor select? Unfortunately, there is no way of
calculating this as it is dependent on the utility function of the investor. The term utility is
derived from economics and refers to the subjective satisfaction obtained by an individual
from taking certain actions or being subjected to certain circumstances. The well-known
concept of diminishing marginal utility implies that, as expected investment return
increases, the additional subjective satisfaction of an investor declines at an increasing
rate. The rate of decline is dependent upon the attitude toward risk of the individual
investor. The more risk-averse an individual is, the steeper the decline in marginal utility
will be. This is illustrated in Figure 4.6.
Figure 4.6 Utility curves
From Figure 4.6 it is clear that the risk-indifferent individual displays no diminishing
marginal utility, i.e. he or she continues to derive utility proportional to the increase in
expected investment returns. The utility function is, therefore, linear. The moderately riskaverse individual requires increasingly higher returns in order to enjoy a given level of utility
– the curve therefore adopts a convex shape. The extremely risk-averse investor’s curve
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slopes even more steeply upward, indicating the relatively greater increase in expected
return required for a given quantum of utility.
The straight line and curves in Figure 4.6 are also known as indifference curves. This means
that individuals represented by those curves are indifferent to investment opportunities
offering the combination of return and utility lying along their particular slope. It is important
to note that it is the slope, or steepness, of the line that distinguishes the risk characteristics
of individual investors.
The utility functions can be superimposed onto the risk-return space illustrated in Figure
4.7. Figure 4.7 indicates the indifference curves for two investors X and Y.
Figure 4.7 Indifference functions
The following can be seen in Figure 4.7:
■■ Three discrete indifference curves of investor X are X1, X2, and X3. The curves proceed
in an upward and leftward direction, depicting the increasing return being sought for
increased risk. The slope of the curve reflects the risk preference of the investor. Curve
X1 does not encounter any investment opportunity. Curve X2, although offering less
utility, is the first to contact the opportunity set of feasible portfolios on the efficient
frontier. Curve X3 meets the efficient frontier at two points, although both points offer
less utility than point X. Investor X will select the portfolio represented by point X.
■■ The indifference curves illustrated for investor Y are Y1, Y2, and Y3. Investor Y is
more risk averse than investor X. This is evident from the fact that the utility curves
of investor Y are steeper, with a greater return required for accepting each unit of
risk than X. As a result, a portfolio will be selected by Y, which has less risk than that
selected by X. It will, however, also have a lower expected return.
2 MULTIPLE-SHARE PORTFOLIO RISK AND RETURN
The principles relating to the calculation of the expected return and the risk of a portfolio
with more than two shares are identical to those of a two-share portfolio as per Formula 4.4.
The expected return is the weighted average of the expected returns of all the shares in the
portfolio. The relevant formula is thus Formula 4.1.
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The risk of a multiple-share portfolio, although identical in principle to that of a two-share
portfolio, is considerably more onerous to calculate. If, for example, 40 shares are held, the
variance matrix will have 1 600 blocks. For each share held, its variance (weighted by the
square of the proportion invested in that share), plus its covariance with every other share
in the portfolio (weighted by the product of the proportions invested) has to be calculated.
For a portfolio of 40 shares, 40 variances plus 780 covariances (each appearing twice) would
have to be calculated.
More formally, a two asset portfolio comprises of a 2 × 2 matrix. Similarly a three asset
portfolio comprises of a 3 × 3 matrix. It follows that a forty asset portfolio comprises of a
40 × 40 matrix. This matrix contains n terms. In the above example, n represents the individual
asset variances. The remaining (n2 – n) terms comprises the covariances between portfolio assets.
(n2 – n) = (402 – 40) = 1 560
or
1560/2 = 780, as each covariance appears twice.
From the formula which follows, it can be seen that the first term is the sum of all the
variances, and the second term is the sum of all the covariances.
n

​2p​= ​
i=1
2
n
n
i=1
j=1
i= j
​ ​​​  ​ ​ ​W W cov ​ ​​  W​i ​​2i ​+ 2 ​
i
j
ij
(Formula 4.6)
where: ​2p​= the portfolio variance
​2i ​= the variance of share i
Wi and Wj = the proportions invested in share i and share j respectively
covij = the covariance between the returns of shares i and j
The opportunity set of all portfolios of shares on a market such as the ASX can now be
graphed as in Figure 4.8.
Figure 4.8 Opportunity set of share portfolios
The shaded area represents portfolios of shares available.
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The following should be noted from Figure 4.8:
■■ A, C, D and E are individual shares, which are portfolios of one share.
■■ The scalloped line AEDC results from the portfolio effect from two-share portfolios of
AE, ED and DC respectively.
■■ All possible portfolios, in the feasible set F (the shaded area), are dominated by the
portfolios that lie along AB, the efficient frontier. This means that, for any portfolio
within the feasible set F, the portfolios along the line AB will offer a superior return
to those vertically below the line, for the same risk. (For example, portfolio X offers a
higher return than portfolio Y, for the same risk.)
■■ Investors will invest only in portfolios that lie along the efficient frontier. The portfolio
which they will select (that is, the specific point along line AB) will be a function of their
risk preference as determined by their indifference curves.
The benefits of diversification
It is evident from the preceding discussion that investors can benefit from allocating their
funds to more than a single investment. This process of diversification has the effect of
reducing the variability of the portfolio returns. Stated differently, the expected return of a
portfolio will be the weighted average of returns, but the risk will be less than the weighted
average of the variances. In general, it has been shown from research studies that a relatively
small number of shares are required in a portfolio in order to derive the major benefit of
reduced risk. This is illustrated in Figure 4.9, which also introduces some important concepts
of risk. These form the basis of the remainder of this chapter.
Figure 4.9 Effect of diversification – portfolio risk
The following can be seen from Figure 4.9:
■■ The risk of the portfolio decreases rapidly with the first few shares held and then levels
off until there is no meaningful reduction in risk resulting from an increase in the
number of different shares in the portfolio.
■■ Using eight shares as an example, and reading off line ABC, the total risk of this
portfolio is in the region of 30%.
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■■
■■
■■
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By enlarging the portfolio to, say, 20 shares, further benefit can be derived in
risk reduction, whereafter the marginal benefits of further diversification become
considerably reduced.
A point is reached where all the shares in the market could hypothetically be held. At
this point the investor is still exposed to some risk. A market-portfolio risk of 20% is
assumed in this example.
It is useful to distinguish between the two kinds of risk. Specific risk relates to variability
in returns caused by factors unique to the company, such as the type of industry in
which it operates and the product it sells. This is often referred to as unsystematic
diversifiable risk, or company risk. An investor may eliminate this type of risk by
diversification.
The remaining risk results from the vagaries of market sentiment and of economic
cycles. It is influenced by factors such as inflation, varying interest rates and foreign
exchange rates. All companies, although not equally sensitive to these economic
fluctuations, nevertheless tend to be affected in a similar way. This type of risk is
generally referred to as systematic risk, non-diversifiable risk or market risk, and cannot
be eliminated by diversification.
Introducing a risk-free asset
Assumptions have been made in presenting the case for diversification, and these assumptions
underlie a model developed from the work of Markowitz (1959) and Sharpe (1964), generally
referred to as modern portfolio theory (MPT).
Like most models, the assumptions do not perfectly reflect reality. However, the model
can be tested by relaxing the assumptions and determining whether the results obtained are
similar to those obtained when applying the assumptions. If this is seen to be the case, the
model is considered to be robust, and to be a reasonable representation of reality. The MPT
model discussed so far is based on the following significant assumptions:
■■ All investors are rational and prefer less risk rather than more for a given rate of return.
■■ All investors have full and equal access to all available information which results in
them all having similar expectations.
■■ There are no transaction costs such as brokerage; the markets are perfectly competitive;
and all financial assets are divisible.
■■ There is no taxation.
Sharpe (1964) introduced the concept of a risk-free asset together with the assumption that
investors can borrow or lend at the risk-free rate. By introducing the risk-free asset, a new
dimension of thought about the capital market was made possible. The effect of introducing
a risk-free asset such as a treasury bill is illustrated in Figure 4.10.
The following should be noted in Figure 4.10:
■■ Rf is the risk-free rate at which investors can borrow or lend.
■■ RfMC is known as the capital market line (CML). It is a tangent to the efficient frontier
EF, with M being the market portfolio – i.e. it contains all the financial assets available
in the market, proportional to the value of the individual’s portfolio.
■■ The point L1 represents the portfolio that could be held by an investor L if there
were no riskless assets available, and represents a rational choice. However, with the
introduction of a risk-free asset, it is clear that investor L could include a proportion of
the risk-free asset into the portfolio and move vertically up to point P, thereby enjoying
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
Figure 4.10 The capital market line
■■
■■
■■
g reater expected return for the identical risk at point L1. However, investor L will act in
accordance with his or her particular utility function, thus selecting point L2 rather than
point P.
The point L2 represents a point to which investor L could move, based on the
indifference curves. At this point, investor L will invest partly in the market portfolio
M and will invest (lend) the remainder at the risk-free rate. By so doing, higher utility
is achieved as a result of being exposed to lower risk than would have existed had
portfolio L1 been purchased.
It is of fundamental importance to note that investor L is investing in a combination of
the market portfolio M and the risk-free asset R. The proportion of each is dependent
upon the point of tangency with line RfMC. The closer to point Rf, the greater the
proportion invested in the risk-free asset.
Similarly, the point B1 represents the portfolio a less risk-averse investor B would
acquire if there were no risk-free asset available. However, with the introduction of
the risk-free asset, B will borrow at the risk-free rate and invest personal funds as well
as the borrowed funds into the market portfolio M. This results in a move to a higher
indifference curve at point B2. B has thus levered a portfolio by borrowing at the riskfree rate with an obligation to pay interest on the borrowed funds, but investing them
together with personal funds in the market portfolio, thus increasing the net expected
return.
Example 4.4: Including a risk-free asset in the portfolio
An investor has indifference curves so that her portfolio has Rp = 25% and p = 17% before
there is a risk-free asset available on the market. The return on the market Rm = 22%, and
the standard deviation of the market, m = 12%. A riskless asset becomes available so that
Rf = 12%, and she is able to borrow or lend at that rate. She has an amount of R10 000
available to invest.
This investor is less risk-averse than the average investor (will accept more risk). She can
benefit from borrowing and levering her portfolio. If she decides to borrow an additional
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R5 000, her new expected return as a result of borrowing may be calculated using the
following general formula:
Rpl = WRf + (1 – W)Rm(Formula 4.7)
where: Rpl = the expected return on a leveraged portfolio
W = the percentage of the investor’s own funds invested in the risk-free
asset (borrowed or lent)
Note that the investor is borrowing in order to invest more money in the market portfolio.
In this case, therefore, W is a negative variable as it indicates the payment of interest which
will have to be made.
Applying Formula 4.7, the expected return on a leveraged portfolio is:
Rpl = WRf + (1 – W)Rm
Rpl = (–0.5 × 0.12) + (1.5 × 0.22)
= 27%
The investor therefore expects to receive a return of 22% on R15 000 and will have to pay
interest at 12% on R5 000. A quick check using the actual figures proves this:
Received: 22% × R15 000 = 3 300
Paid: 12% × R5 000 = –600
Return on investment of R10 000
= 2 700
In order to establish the risk of the new portfolio, Formulae 4.6 or 4.5 for risk of a two-asset
portfolio are appropriate, the market portfolio being considered as one asset and the riskfree asset as the other. Because the risk-free asset has  = 0, the formula loses two of its
terms and simplifies to:

pl = ​ W​m2 ​ ​ ​m2 ​ ​(Formula 4.8)

= Wmm = 1.5 × 0.12
= 18%
The investor, by using the borrowing facility, has levered herself from Rp = 25% and p =
17% to Rpl = 27% and pl = 18% which offers higher utility to her.
In much the same way, an investor who is more risk-averse than average (prefers less
risk), could invest a proportion of available funds into the risk-free asset. The result would
be to move down the line RfMC to a point such as L2 in Figure 4.11, which would place the
investor on a higher utility curve than at point L1. It is clear from Figure 4.11 that all points
along the capital market line in fact dominate the efficient frontier, except point M (the
market portfolio, an unlevered portfolio comprising only shares and no riskless asset).
3 BETA ANALYSIS
Modern portfolio theory is one of the most important developments in finance theory. The
theory does, however, have practical shortcomings. Firstly, the determination of portfolio
risk of a multishare portfolio is extremely onerous. Secondly, the notion that investors
would, in practice, purchase a proportion of all the shares in the market is impractical,
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although investment in some unit trusts or by buying the all-share index may be comparable
to investment in a market portfolio.
It has already been noted that great benefit in risk reduction is achieved by diversifying
into a relatively small number of different shares and that the marginal benefit of further
risk reduction soon becomes negligible. It has also been noted that company-specific risk,
also referred to as unsystematic risk, is the element which can be diversified away, whereas
investors always remain subject to market risk. Sharpe recognised these shortcomings and
devised a measure that reflects the sensitivity of an individual share to fluctuations in the
market, thereby measuring the share’s non-diversifiable risk. The measure is known as the
beta of a share.
Because investors will not be rewarded for risk that can be eliminated by diversification,
only the market risk as measured by beta is relevant. The measure is called beta because it
is represented by the term b in the straight line equation y = a + bx – i.e. it is the slope of a
line representing the returns on a given share when compared with the returns of the share
market as a whole. This is reflected in Figure 4.11.
Figure 4.11 Graphic representation of beta
By definition, the market has a beta of one. For example, a share which on average increases its
return by 10% when the market returns increase by 10%, and vice versa, will also have a beta
of one. If a share increases on average by 15% when the market increases by 10%, it has a
beta of 1.5. If a share increases on average by 5% when the market increases by 10% it has a beta
of 0.5. Beta is thus a measure of the volatility of a share relative to the volatility of the whole
share market.
Beta as a measure of portfolio risk
It must be stressed that the future beta of a share is the relevant measure of its market risk.
However, the beta is established from past information on the assumption that it will remain
fairly stable over time. The total risk of any individual share is:
Total risk = Systematic (market) risk + Unsystematic (specific) risk
As unsystematic risk can be eliminated by diversification, the risk which is of interest to the
investor is the systematic risk as measured by the beta of the portfolio.
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The major advantage arising from the use of beta analysis is that the beta of a portfolio of
shares is simply the weighted-average of the individual share betas, expressed as follows:
n

p = ​ ​ ​​  Wjj(Formula 4.9)
j=1
where: Wj = the weight of share j in the portfolio
It is now possible to establish the two parameters of risk and return for a portfolio quite
easily, provided the betas of the individual shares are known. Investors will therefore manage
their portfolios by selecting a portfolio which has a beta that provides them with maximum
utility. As beta is a linear concept, it is possible to graph a security market line (SML) which is
used for displaying the risk-return relationship for individual shares held within a diversified
portfolio. The formula for the SML, which is known as the Capital Asset Pricing Model is:
Ri = Rf + i(Rm – Rf)(Formula 4.10)
where:
Ri = the required return on share i
Rf = the risk-free rate
i = the beta of share i
Rm = the expected return on the market as a whole
It is apparent that, for given shares, the premium for risk (Rm – Rf) will be greater as beta
increases because that share is more volatile (risky) than the market average. The SML is
illustrated in Figure 4.12.
Figure 4.12 The security market line
The expected return of all shares will fall along the SML. This pricing model, known as the
capital asset pricing model (CAPM), makes it possible for investors to create and adjust
portfolios of their choice. Any individual share that does not plot along the SML is either
overpriced or underpriced because its expected return differs from its required return, thus
requiring a price adjustment to restore equilibrium. If the market is functioning efficiently,
the forces of supply and demand will restore the price to equilibrium, on the SML.
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Example 4.5: Portfolio management
An investor holds a portfolio of 20 shares with an expected return of 28% and a beta of 1.3. He
wants to withdraw 25% of the funds currently invested in share A, which has Ra = 24% and
βa = 0.9, and invest them into share B, which has Rb = 35% and βb = 2.0. What is the
expected return and beta of the new portfolio?
The expected return of the remaining 75% of the portfolio must first be determined as
follows:
28% = (0.25 × 24%) + (0.75 × Rx)
The expected return on the remaining 75% of the portfolio Rx is calculated as follows:
Rx = [28% – (0.25 × 24%)] / 0.75 = 29.3%
The expected return of the new portfolio will be:
Rpn = (0.75 × 29.3%) + (0.25 × 35%)
= 30.725%
Similarly the beta of the remaining 75% of the portfolio must first be determined as
follows:
1.3 = (0.25 × 0.9) + (0.75 × βx)
The beta of the remaining 75% of the portfolio is βx and is calculated as follows:
βx = [1.3 – (0.25 × 0.9)] / 0.75 = 1.43
The beta of the new portfolio will be:
βpn = (0.75 × 1.43) + (0.25 × 2)
= 1.5725
Beta and the capital asset pricing model (CAPM)
In statistical terms, beta is a regression co-efficient expressing the relationship between an
individual share and the market with the variance of the market, and it can be determined
through least squares regression analysis. Usually weekly or monthly returns are used over
a period of years for the company’s shares. For a measure of the market as a whole, the
market index is used. The procedures for calculating beta are demonstrated in Appendix
4.1. In Appendix 4.2, Obeid Mahomed and Dave Bradfield offer us their perspectives on the
determination of betas for the AIFMRM Equity Risk Service (previously the BNP Paribas/
Cadiz Equity Risk Service), which is an important provider of betas to practitioners. Betas
for South African companies may also be sourced from other services such as Bloomberg,
Reuters and McGregor BFA. We have set out betas sourced from both AIFMRM and
Bloomberg in Table 4.10. The Bloomberg betas and the AIFMRM betas differ as AIFMRM’s
betas are based on monthly data over 5 years whilst Bloomberg betas are based on weekly data
over 2 years. AIFMRM also adjusts for thin trading. It is important to apply judgement in
selecting a beta service. Different researchers may arrive at different betas depending on the
method of calculation employed, the number of past observations, and other assumptions
that have to be made. Betas may be established for individual shares as well as for industry
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sectors. Betas are subject to fluctuation, although portfolio betas have been found to be
fairly stable over time.
Table 4.10 illustrates betas calculated for sectors on the JSE. A Bloomberg beta of 1.29
for the General Mining sector indicates that this sector is relatively more volatile than the
overall index. This means that if the overall market changes by 1%, then the General Mining
sector changes in the same direction by 1.29%. Betas for some sectors are larger than others.
Food and Drug retailers are on the other side of the beta spectrum, with an industry beta
of 0.46. This is significantly lower than the market beta of one and reflects the lower risk of
investing in this sector. Food and drug retailers are expected to offer stable cash flows. Some
other betas seem to offer questionable results and we need to apply betas with a degree of
judgement and understanding of the underlying statistical dimensions of the data employed.
Table 4.10 JSE Beta analysis
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In South Africa, the resources sector constitutes close to 20% of the market capitalisation
of the JSE. This means that the betas of firms outside the resources sector will be lower in
relation to the All Share Index because of the resources sector and its higher volatility.
Returns are measured as a percentage increase or decrease in the share price (plus
dividends received) at the end of the month, if monthly readings are taken, over the share
price at the end of the previous month. The equation for finding the beta of a company in
simple regression form if monthly data are used is:
Ri
where: Ri
α
βi
Rm
e
= α + βi(Rm) + e(Formula 4.11)
= the monthly return on the share i
= the intercept on the vertical axis
= the slope of the regression line for share i
= the monthly return on the market
= a random error term
In order to find β, the usual statistical procedures for regression are required, solving for α
(alpha) and β (beta). It should be noted that the random error term e is expected to be zero
as random errors should sum to zero. The intercept alpha should also be zero when excess
returns are used. Any deviation from zero in the alpha indicates that the share has at some
time been inefficiently priced, a situation which is unlikely to persist if the market is efficient.
Figure 4.13 illustrates the process used to establish the beta of share i. Monthly readings
have been taken of the return on the market as measured by the change in the market index
and plotted against the returns on share i, adapted for monthly returns. It is clear that share
i has a low beta, probably in the region of 0.5. Its low beta results from the fact that it is
clearly less volatile than the market as a whole. Investors would therefore expect to receive
a return less than that of the market. The line has an alpha which is greater than zero in this
instance, indicating a price appreciation over this period which was in excess of that of the
market as a whole. In general, this relative appreciation will not be expected to continue
indefinitely.
Figure 4.13 Regression analysis to establish market risk (beta)
Once the beta of an individual share is known, it is relatively easy to apply the CAPM since
the risk-free rate and expected return on the market are usually readily available.
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Example 4.6: Capital asset pricing model
An investor wants to add shares in Investgro Ltd to her portfolio. Investgro has a beta of
0.5, the risk-free rate is 7%, and the return on the market is 12%. Establish the expected
return on Investgro.
Using Formula 4.10:
Ri = Rf + βi (Rm – Rf)
= 0.07 + 0.50(0.12 – 0.07)
= 9.5%
The expected return on Investgro Ltd, as anticipated, is less than the 12% expected return on
the market. The investor would now attempt to establish whether the actual return is likely to
be higher or lower than 9.5%. If it is likely to be higher, the share is underpriced and should be
bought. Using the SML, the relationship can be plotted and Investgro’s position established as
in Figure 4.14.
Figure 4.14 SML to plot share i
CAPM is an elegant theory which is based on some restrictive assumptions. As we relax some of
these assumptions we come into contact with reality. The CAPM offers a valuable framework
for analysing risk and return but we need to reflect on its practical usefulness by evaluating the
assumption of perfect capital markets or efficient markets.
4 THE EFFICIENT MARKETS HYPOTHESIS
Perhaps the most significant assumption of modern portfolio theory and the CAPM is the
assumption of perfect capital markets. In a less rigorous form, the assumption is that all
capital markets are efficient. The efficient market hypothesis (EMH) posits that a company’s
share price reflects all available information. Fama (1970) suggested three forms of market
efficiency.
The weak form
The first level of efficiency, known as the weak form of the EMH, holds that share-market prices
follow a random walk. This is likened to the path of a drunk where it is impossible to predict
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whether the next step will be to the left or right. The information impounded in the share
prices is thus considered to fully reflect the historic price sequence of each individual share. As
a result, it follows that price changes are independent of one another, making it impossible to
predict a future price based on a series of past prices. In terms of the weak form of the EMH
it should not be possible to employ trends, charting, technical analysis and past movements in
share prices to earn superior returns.
The semi-strong form
The semi-strong form of the EMH holds that all publicly available information about a share
is impounded immediately and without bias into the share price. The historic price sequence
is also included in the information set. It is not possible to use fundamental analysis, such as
the analysis of financial statements, to earn superior returns. This is because such information
has already been absorbed by the market and is immediately reflected in a price change.
The share price reflects all publicly available information. Only with inside information is it
possible to identify shares that are incorrectly priced.
An interesting aspect of efficiency is that it requires the presence of investors who do not
accept the efficiency of the market. As a result, they are engaging in fundamental analysis in
an attempt to discover new information. This activity in turn contributes to market efficiency.
The strong form
The third level of efficiency, known as the strong form, holds that all information, both privately
and publicly held, is impounded into the share price immediately and without bias. Thus
it is impossible for any investor to consistently outperform the market, even with “inside”
information.
Market efficiency: the evidence
The evidence about market efficiency is mixed and complex. Some of the evidence that
supports market efficiency includes the following findings:
■■ Although there is some relation between movements in share prices over short
horizons, these are not sufficient to cover trading costs. This supports the weak form of
market efficiency.
■■ Share prices react quickly and in the right direction to new information that is price
sensitive such as mergers and acquisitions, earnings and dividend announcements.
■■ Professional fund managers on average have not been able to beat the market index
after fees.
What is the evidence that indicates that markets are not efficient? This is where it gets hard,
for either markets are inefficient or, alternatively, CAPM does not capture all the relevant risk
factors. We will present these for now as market anomalies:
■■ When we analyse price movements over 3- to 9-month holding periods, we find a
momentum effect as companies that have done well will continue to do well and
companies that have done poorly will continue to do poorly in later periods – over a
subsequent period of about 3 years. Investing in a portfolio of the best performing
shares over the last six months and undertaking short sales of the worst performing
shares over the previous six months will result in positive returns relative to other
shares. Therefore, there seems to be evidence of a momentum effect over periods of
about three years. The indication here is to invest in past winners and short past losers.
■■ Over longer multi-year periods, we find that there may be negative long-term
performance effects. This means that companies that have performed poorly over long
periods of 3 or 4 years will see a reversal of fortune and will do well in a subsequent
period whilst companies that have performed strongly over a period of three or
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■■
■■
■■
■■
FINANCIAL MANAGEMENT
four years will perform poorly in the years thereafter. This effect is also called mean
reversion. This leads to a contrarian investment philosophy whereby it pays to buy
the long-term losers and sell the long-term winners. This may indicate that there is
overreaction over intermediate horizons, leading to the momentum effect, which is then
followed by a long-term reversal as investors come to terms with past overreactions to
positive and negative news.
A portfolio of low price-earnings (P/E) shares have generated higher returns than
a portfolio of high P/E ratio shares. This could be because low P/E ratio companies
involve higher risks not captured by CAPM betas.
Neglected firms are firms not covered by the large institutional investors nor researched
by brokers and analysts. Neglected firms and small firms tend to earn higher returns
than that predicted by CAPM. This again may indicate that the risks of investing in
small firms and neglected firms, where there is little research or information or liquidity,
will increase investment risk which means a higher return is justified.
An investment strategy of investing in firms with high book-to-market value of equity
ratios will result in higher returns.
Although share prices react quickly to earnings announcements, companies that report
positive earnings experience a subsequent upward drift in share returns whilst negative
earnings announcements may result in a downward drift in subsequent returns.
It would be naïve to expect that inside information will not lead to abnormal profits. This is
why there should be and there are penalties for trading on the basis of inside information.
Value shares, which are shares with high book-to-market ratios, low P/E ratios and
depressed share prices, were found to have offered higher returns than high-growth shares.
Size effects, momentum and high book-to-market ratios have been found to apply in securities
exchanges across many countries. Fama & French indicate that these factors are proxies for
risk and they have added book-to-market and size factors to capture the required return. This
extends CAPM by adding these two factors to the model and is referred to as the Fama-French
Three-Factor Model. We set this out in Chapter 7.
It is important to note that some of these anomalies have since gone missing. Some
anomalies do not seem to stand the test of time and the publication of such anomalies can
have an effect on the effectiveness of these anomalies thereafter. To conclude, we would state
that the evidence for market efficiency is mixed and we will set out how firms adjust the CAPM
cost of equity in Chapter 7.
Evidence of the efficiency of the JSE
The weak form of the EMH was found to apply on the JSE on the basis of analysing shortterm movements in share prices. Van Rensburg and Robertson3 have indicated that the small
size effect holds for the JSE and investing in low price-earnings companies will offer higher
returns than indicated by CAPM. Applying the Fama-French Three-Factor Model seems
to explain the returns of companies on the JSE. McKane and Britten4 reported a significant
liquidity premium for the JSE in that investors require a higher return for holding illiquid
shares. The JSE is significantly less liquid than the major securities exchanges and there are
closely held and thinly traded shares. Even relatively large and well-known companies may not
trade each day of the year and we have set out some of these companies with their percentage
of days traded. This does not even consider the impact of volumes on pricing and only reflects
Van Rensburg, P. and Robertson, M. (2003) Size, price-to-earnings and beta on the JSE, Investment Analyst
Journal, 58, 7–16.
4
McKane, G. and Britten, J. (2018) Liquidity and size effects on the JSE, Investment Analysts Journal, 47 (3)
229–242.
3
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whether there was trading in the shares each day of the year. Investors require higher longterm returns for holding relatively illiquid shares.
How have professional fund managers performed in South Africa? In a study by Wessels and
Krige5, it was found that although fund managers were able to achieve short-term quarterto-quarter persistence in returns, the longer-term persistence in performance tended to
disappear. Bradfield and Swartz6 found that the top quartile funds indicated a high degree
of persistence of returns from quarter to quarter. However, persistence declined over longer
periods. However, there were a few funds that exhibited persistence in either outperforming
or underperforming the ALSI.
Let’s evaluate for example the investment performance of Allan Gray. In the 44 years
to 30 June 2018, Allan Gray Equity has managed to achieve an annualised return of 25.6%
as compared to the annualised return of 16.9% for the ALSI. This has been achieved at a
slightly lower level of risk. The evidence is that most managers are unable to beat the market
index, but there are a few exceptions. However, we need to understand that Allan Gray is
active sometimes in affecting managerial performance and decisions.
What about passive investing in South Africa? For example, investors are able to invest
in the Satrix 40 index fund which is offered by the JSE at a very low cost, and passive index
fund investing is expected to grow in South Africa.
Is the CAPM used in practice?
Yes. In a PWC survey of South African investment professionals, it was found that the CAPM
is by far the most dominant method used in practice to determine a company’s cost of equity.
The CAPM is based on the use of betas, and Bloomberg and the AIFMRM Equity Risk Service
are the most popular sources of betas. The use of betas in determining the cost of equity is
dominant in South Africa and in many other countries such as the USA, the UK and Australia.
Yet, Warren Buffett thinks differently. As he states in one of his letters to his shareholders:
To invest successfully, you need not understand beta, efficient markets, modern portfolio
theory, option pricing or emerging markets.
What do we think? The use of betas makes sense but we may need to apply judgement in
particular cases by analysing the underlying data and we need to take care not to double
count for risk. Further, there are other issues in determining the cost of equity and we will
come back to this when we study the cost of capital in Chapter 7.
Does CAPM work? The evidence from empirical studies is that we need to extend CAPM in
order to explain share returns adequately. The SML is flatter than indicated by CAPM. FamaFrench (1992) was able to increase the accuracy of predicting share returns significantly by
including size and value factors, as well as a market beta factor. Small companies and companies
with high book values relative to their share price (value shares) tend to produce higher returns
Wessels, DR and Krige, JD (2005). The persistence of active fund management performance, SA Journal of
Business Management, 36(2).
6
Bradfield, D and Swartz, J (2001). Recent evidence on the persistence of fund performance – a note. SA Journal
of Accounting Research, 15(2).
5
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than indicated by beta alone and according to Fama-French, these represent risk factors. There
are therefore three sources of risk – market risk, size risk (investing in smaller companies
implies higher risk) and low book-to-market ratios (which will often include companies that are
experiencing financial distress or changes to their business models). The Fama-French ThreeFactor Model includes a market beta factor, as in CAPM, and then includes a size factor and
a value factor to predict a company’s expected/required return. In the annexure to Chapter
7, we explain this model in greater detail and we also indicate how practitioners make ad-hoc
adjustments to CAPM to take into account these factors in determining a required return.
5 EXCHANGE TRADED FUNDS (ETFs) AND UNIT TRUSTS
In order to acquire an investment that replicates the performance of the JSE All Share or the
JSE Top 40 index, an investor would need to buy all the shares making up the JSE All Share
or the JSE Top 40 index. A small investor may not have sufficient funds to achieve this and
transaction costs would be high. Yet, an investor may wish to invest in a portfolio of shares to
attain diversification.
In order to achieve effective diversification, the investor may invest and acquire units in a
unit trust such as the Allan Gray Equity Fund. You send your money to Allan Gray and this
is combined with the contributions from other investors to acquire shares in companies. You
do this by purchasing units in a unit trust at its net asset value which reflects the values of the
underlying equity investments owned by the unit trust at the end of each day. As the unit trust
receives funds from investors, it purchases shares in line with its investment policy. An index
fund which tracks the JSE Top 40 would purchase shares in the JSE Top 40 companies in line
with their market value weightings in the index. If many investors wish to withdraw funds then
the unit trust will need to sell shares in order to meet its redemption obligations. A fund will
retain a small percentage of its funds in cash in order to meet liquidity requirements and meet
redemptions but when markets fall and many investors withdraw funds from a unit trust at the
same time, then the unit trust will need to sell shares which can then further accentuate the
selling pressure on shares. This makes a unit trust an open-ended investment entity.
Exchange Traded Funds (ETFs) are similar to unit trusts but are listed on the JSE.
Essentially an investor can acquire shares in an ETF which owns a portfolio of shares or bonds
or commodities. Investors are able to trade ETFs like any other share on the JSE but the
ETF represents ownership of a portfolio of assets which may offer an investor the benefits of
diversification at a low cost. A commodity ETF will invest in gold bullion, or platinum or another
commodity. If an investor wished to invest in gold, then often the investor would either need
to invest in physical gold which is not practical7 or more likely acquire shares in gold mining
companies such as Gold Fields. However, an investor may not wish to be exposed to the risks of
gold mining in regard to changing ore grades, higher operating costs, production disruption due
to seismic activity, industrial action and regulatory risks. An investor may simply acquire shares
or debentures in a gold ETF which acquires gold bullion, and the value of the gold ETF will
reflect the underlying value of its gold holdings as the gold price moves up and down.
Another ETF may simply reflect an index such as the JSE Top 40 index. The advantages of
investing in an ETF include diversification, flexibility with regard to trading, low costs, liquidity
and transparency. An index ETF simply replicates the underlying index, which requires no
active management and therefore costs are low. The Satrix Top 40 ETF has a cost of 0.10%
(but there are trading costs) whilst the Satrix Top 40 Unit Trust has a direct cost of 0.45% plus
VAT (in 2018). An actively managed equity unit trust fund may involve fees to investors of
about 1.5% to 2.2% of the funds under management per year.
You can buy gold coins such as Krugerrands but trading costs are high and there are insurance costs and storage
costs, although it may be reassuring to touch the gold you own.
7
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The largest gold ETF is the NewGold Exchange Traded Fund managed by ABSA’s CIB
division. ABSA states the following about NewGold;
Absa CIB’s NewGold Exchange Traded Fund (NewGold) is one of the simplest and cost-efficient
methods for investors to invest directly in actual gold. NewGold continuously tracks the gold spot price
and enables investors to invest in a listed instrument (structured as a debenture) in which each security
is equivalent to approximately 1/100th ounces of gold and is fully backed by holdings of gold bullion
The NewGold ETF had a total NAV of over R12.5bn in 2018 and the ETF holds 728 750oz
(22 670 kg) of physical gold bullion. The annualised total expense ratio is 0.4%.
Let’s analyse a possible scenario. Thabisa and Zanele are Chartered Accountants and
friends who decided in 2008 to invest R1m each in gold. Thabisa decided to invest her R1m in
the NewGold ETF. Zanele decided to invest her R1m evenly across three major gold mining
companies, Gold Fields, AngloGold and Harmony. Ten years later, on 12 October 2018 you
plot how they have done with their gold investments. This is presented in Figure 4.15.
Figure 4.15 Investing in Gold: NewGold ETF versus gold mining company shares
Thabisa would in October 2018 have R2.37m whilst Zanele would only have about R347 000
[(0.43+0.35+0.26)/3] even though they both started with R1m each. Zanele would have
endured the risks of gold mining, whilst Thabisa was only exposed to the risk of the underlying
gold price movements8. This indicates the potential value of ETFs to portfolio management.
Satrix manages over R80bn of index tracking assets and provides investors the ability to
invest in very low-cost index funds and ETFs. For example, it offers investors access to the
Satrix 40 fund and Satrix 40 ETF. Satrix states the following:
The Satrix 40 fund tracks the performance of the FTSE/JSE Top 40 Index which represents the
40 largest companies by market cap. It endeavours to accurately replicate the index by holding all
constituents in the exact index weighting. The index is rebalanced quarterly and the fund therefore
incurs minimal trading fees as a result of low turnover. This fund is ideal for investors who seek
general market performance while minimising trading costs.
The standard deviation of monthly returns for the NewGold ETF was 10.5%, whilst for Gold Fields it was
15.1%, for AngloGold it was 16.2% and for Harmony it was 20%. The NewGold ETF offered a higher return
at a lower risk over this period. The compound annualised growth rates were as follows: NewGold 8.4%, Gold
Fields –10.2%, AngloGold –8.2% and Harmony –13%. When we use arithmetic means, we find that Harmony has
a positive average return as well as AngloGold, which indicates the effect that volatility can have on arithmetic
means. Rather focus on the compound annual returns. (See Chapter 3 for more on arithmetic and geometric
(compound) returns.)
8
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The Satrix 40 ETF tracks the performance of the FTSE/JSE Top 40 index which includes the 40
largest companies on the JSE, ranked by investable market cap. The ETF aims to accurately replicate
the index by holding all constituents in the exact index weighting. Distributions are made quarterly.
As ETFs trade as shares, the share price of an ETF can divert away from NAV and sometimes
ETFs may trade at a discount to NAV. For example, assume that the market value of the XYZ
ETF’s holdings adds up to R660m and there are 600m shares in issue. We would expect that the
value of the ETF share price should be R1.10 (660/600). However, it may trade at R1.04 which
is at a discount to NAV but represents the buying and selling actions by investors in the ETF. It
does also mean that management is not obligated to dispose of shares or assets owned by the ETF,
which may be useful during periods of short-term but severe market declines. Investors redeem
their investment by selling their ETF shares on the JSE like any other share. In times of market
stress, there is some evidence that the prices of ETFs may be more volatile than the market.
An ETF will involve brokerage costs and there is a spread between buying and selling rates.
Liquidity may be an issue although ABSA for example may act as a market maker to ensure
liquidity for its ETFs. There are now ETFs for commodities, industry sectors, factor investing
strategies, high-dividend yield shares (e.g. SATRIXDIV), low-volatility shares, emerging
markets and so on. ETFs enable investors to diversify beyond equities and bonds, but investors
should still be cautious with regard to the nature of the underlying assets of any ETF and the
reputation of the issuers9.
FROM THE REAL WORLD
You may ask whether the principles of diversification are relevant in the investment decisions
undertaken by asset managers such as Allan Gray and Coronation. The following are extracts
from their correspondence with their investors, which indicate the importance of diversification
in reducing portfolio risk. Seema Dala of Allan Gray writes:
“Diversification is only useful when the assets being added to the portfolio have low correlations with
the existing assets. As we add asset classes to a portfolio, which have negative or zero correlations to the
assets, which are already in the portfolio, the portfolio becomes more diversified. This should in turn
reduce the volatility, or unpredictability, of portfolio returns.” With regard to developed markets, she
states the following: “… asset classes are highly uncorrelated to the ALSI, so adding these (developed
market) assets to a portfolio of local assets would significantly reduce overall portfolio volatility”
(Quarterly Commentary Q1: March 2013)
Coronation in its Global Capital Plus Portfolio Fund Sheet, as at 31 August 2014, states:
Overall portfolio risk is managed through the inclusion of non-correlated asset classes and
stocks are selected on an equal measure of upside return and downside risk.
SUMMARY
The rationale for investing in a portfolio of shares rather than a single share is based on the
benefit received in the form of risk reduction by diversification. The expected return of a
portfolio is the weighted average return of the shares held in the portfolio. The risk, however,
is not a weighted average of risks because of the effect of less than perfect correlation of
returns among the shares in the portfolio. The capital asset pricing model may be an appropriate
method of pricing individual shares held by a diversified investor. Establishing the beta of a
company enables the effect of that particular share on the overall portfolio to be assessed.
Using beta analysis it is possible to manage a portfolio of shares in accordance with the desired
level of market risk, the specific risk having been eliminated through diversification.
Market efficiency is a fundamental assumption which has significant implications for
financial management.
Exchange Traded Notes (ETNs) are debentures issued by a bank in which the return is directly linked to an index
or commodity. This implies greater risk as it is based on a promise by the bank. What if the bank fails? Although
NewGold has been structured in the form of debentures, there is a separate special purpose company which issues
the debentures and which is independent of ABSA and therefore will not be affected if ABSA fails. In substance,
NewGold is an ETF.
9
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GUIDANCE TO PORTFOLIO MANAGEMENT
By Johnathan Dillon M.Com CA(SA)
Summary of the risk and return concepts linking Chapters 3 and 4
Chapter 3 deals with the concepts of risk and return in relation to a single share, as well as with
the comparison of single shares. Chapter 4 does the same, except in relation to a portfolio of
shares. The table below presents a summary of the pertinent concepts of these chapters relevant
to analysing shares:
RETURN
1 share
RISK
COMPARISON
Standard deviation () or
Co-efficient of variation
Expected return (Re) of
variance ( ) of share
(CV)
share
Or
Or
Beta () of share
z score
2
Standard deviation () or
variance (2) of the
portfolio, calculated as:
2 shares
(portfolio)
___
Weighted average of
p = √
​ ​2p​ ​ ​​
shares’ expected returns
​​2p​​  = ​W​2a​  ​​2a​ ​ ​ + ​W​2b​​
​  2b​ ​​  +
(Rp)
2WaWbcovab
Co-efficient of variation
(CV)
Or
z score
Or
Weighted average of
shares’ betas ()
The standard deviation
() or variance (2) of
the portfolio can be
3+ shares
(portfolio)
Weighted average of
shares’ expected returns
(Rp)
determined using a
Co-efficient of variation
lengthy formula similar to
(CV)
that used under 2 shares
Or
above
z score
Or
Weighted average of
shares’ betas (p)
A summary of important risk symbols is presented in the table below:
SYMBOL
​2​a​ ​
NAME OF SYMBOL
Variance of share a
SUMMARY OF WHAT IT MEASURES
The extent to which the expected returns of the share
deviate from the mean.
The same as what the variance measures – it is
a
Standard deviation of share a
merely the square root of the variance and in a
standarised form.
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SYMBOL
CVa
Covab
NAME OF SYMBOL
SUMMARY OF WHAT IT MEASURES
Co-efficient of variation of
Relates the units of return to the units of risk by
share a
measuring the units of risk per 1% of return.
Co-variance of two shares a
and b
ab OR
Correlation co-efficient of
rab
two shares a and b
The extent to which the returns of two shares move
together and in which direction (that is, the relationship between the returns of the two shares).
The same as what the co-variance measures – it is
merely the standardised form of the co-variance as
it falls between −1 and +1.
The proportion of variability (the goodness of fit)
​r​2ab​​  OR
R2
Co-efficient of determination
between two data sets (in this instance, share
of two shares a and b (also
a returns and share b returns) and is merely the
known as R-squared)
square of the correlation co-efficient; hence, it will
be between 0 and +1.

Beta of a share
The non-diversifiable risk of a share as reflected by
the share’s sensitivity to fluctuations in the market.
The important risks covered in these chapters, as well as how they link together and are measured,
are summarised below:
Total risk for an individual share or portfolio can be expressed as follows:
Total risk = systematic (market) risk + unsystematic (specific) risk
Total risk is measured by calculating the variance or standard deviation of the returns of the
share or portfolio. However, when taking into account the concepts of business and financial
risk covered in Chapter 3, the total risk of an entity that shareholders are exposed to can also be
expressed as follows:
Total risk = business risk + financial risk
A somewhat useful measure of this expression of total risk is the degree of combined leverage
(DCL), which equals contribution divided by profit before tax or the degree of operating leverage
(DOL) multiplied by the degree of financial leverage (DFL). However, as noted in Chapter 3,
the DCL does not entirely measure all facets of business and financial risk. This expression
of total risk also links directly with the asset beta and equity beta concepts covered in greater
detail in Chapters 7 and 10, as well as with the need to “unlever” and “relever” betas in certain
situations.
Systematic risk (also referred to as non-diversifiable or market risk) is the risk that remains after
diversification, that is, the risk of being in the economic system in which the entity operates.
No amount of diversification can eliminate this risk. Systematic risk is measured by calculating
the beta of a portfolio or share’s returns in relation to the returns on a fully diversified market
portfolio.
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Unsystematic risk (also referred to as diversifiable, specific or company risk) is the risk of a
portfolio in excess of the systematic risk. Investors can reduce or even eliminate this risk by
holding more and more shares until the portfolio risk equals the market / systematic risk.
Sovereign risk is essentially the risk of a country based on economic, political and financial
factors, that is, the country’s financial health and creditworthiness, which have a bearing on the
systematic risk of a market. Therefore, the higher the sovereign risk of a country, the higher
the systematic risk of an economic system and consequently the higher the risk of all entities
operating within that particular country.
Business risk is the risk relating to the operating activities of the entity, that is, the risk inherent
in its operations ignoring how the entity’s operations are financed.
Financial risk is the additional risk placed on an entity (and on ordinary shareholders) as a result
of the decision to finance with debt rather than equity.
S
SELF-STUDY PROBLEM
Shares A and B have the following historical dividend and price data:
Required:
(a) Calculate the realised rate of return (or holding-period return) for each share in each
year. Assume an equally weighted portfolio. What would the realised rate of return on
the portfolio be in each year from 20.2 through 20.7? What are the average returns for
each share and for the portfolio?
(b) Calculate the standard deviation of returns for each share and for the portfolio.
(c) Based on the extent to which the portfolio has a lower risk than the shares held individually,
would you assess that the correlation co-efficient between returns on the two shares is
closer to 0.9, 0.0 or – 0.9?
(d) If you added more shares at random to the portfolio, what is the most accurate statement
of what would happen to σp?
– σp would remain constant, or
– σp would decline to somewhere in the vicinity of 15%, or
– σp would decline to zero if enough shares were included.
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Suggested solution
(a) The return to the shareholder for each period for holding a share is calculated as follows:
Dividends for the period + Share price at the end of period
​ – 1
Return = 
​
Share Price at beginning of period
The returns are presented in the following table:
The following are some of the workings of the returns set out in bold in the above table for
year 20.3:
3.40 + 35.50


​– 1 = –20%​
​– 1 = –11.09%
​ 2.00 + 16.00
22.50
43.75
–0.20 + –0.1109

​
​= –15.54%
2
The deviations from the mean return for each year as well as the product of the deviations is
set out in the following table in order that we may determine the variance, standard deviation
for each share as well as the covariance and correlation co-efficient. This is the long way of
doing it and we will also use Excel statistical functions to determine the same results.
The following are some more workings on how we get to the deviations and variance and
covariance calculations for 20.3.
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The squared deviations for Share A, Share B and the Portfolio are simply determined as
follows:
A: (–0.3141)2 = 0.0987
B: (–0.2249)2 = 0.0506
C: (–0.2695)2 = 0.0726
The covariance (product of the deviations of A and B) for 20.3 is (–0.3141)(–0.2249) =
0.0706.
Alternatively, we could also use Formulae 4.2, 4.3 and 4.4:
Correlation co-efficient:
0.0342   ​= 0.8907 (Rounding effect: correl = 0.8914)
​ 
(0.1961)(0.1958)
(b) Variance and standard deviation of portfolio:
(c) Closer to 0.9. The fact that the two shares are very similar in the direction in which
returns move, results in a high correlation co-efficient, resulting in less risk reduction
from investing in both than would have been the case had the correlation co-efficient
been low or negative.
(d) The p would decline to a point which reflects the systematic risk, that is, the risk of the
market. This is certainly not zero. It would also not remain constant, as the more shares
added, the greater would be the effect of less than perfect positive correlation between shares,
reducing portfolio risk. If the market risk is in the region of a standard deviation of 15%
(which seems reasonable), this is the most likely figure to which the portfolio risk will decline.
APPENDIX 4.1 CALCULATING THE BETA CO-EFFICIENT
Beta has been defined as the sensitivity of an individual share to changes in the index of the
stock market as a whole. The market as a whole has a beta of one. Individual shares will thus
have betas reflecting their relative sensitivities to the market beta of 1. An individual share,
for example, which increases in price on average by 15% when the market index rises by 10%
and the risk-free rate is constant, will have a beta of 1.5. Beta has a special application in the
capital asset pricing model in the expression:
Rj = Rf + βj (Rm – Rf)
(Formula 4.12)
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where: Rj = the return expected on share j
Rf = the risk-free rate of return
Rm = the return expected on the market
βj = the percentage change in an individual share’s return for a 1%
change in the market return
βj, in turn, can mathematically be expressed as:
Covjm
rjmjm
βj = ​ _____ ​ = ​ _______
​
(Formula 4.13)
Varm
 2m
where:
rjmjm = the covariance of share j’s return with the market return (also
written as covjm)
m2 = the variance of the market return
Modern portfolio theory suggests that covariance with the market is the only relevant risk,
as unsystematic or specific company risk is virtually eliminated through diversification into
a portfolio of shares. Beta reflects the covariance of an individual share with the market,
standardised by dividing this covariance by the market variance. It is thus the only relevant
measure of the risk of an individual share held by an investor in a portfolio.
Despite criticisms and counter evidence, the CAPM remains a widely used model. For
example, services such as Bloomberg regularly publish beta co-efficients for securities quoted
on the NYSE while, for example, the BNP Paribas/Cadiz Equity Risk Service has regularly
updated such co-efficients for companies listed on the JSE.
Despite the fact that betas are available for many South African shares, some analysts
prefer to calculate betas based on the most recent series of price and market data. Judgement
is involved in applying the techniques for calculating the beta of a share. However, the beta is
in essence simply a regression co-efficient reflecting the slope of a straight line graph regressing
the excess returns of an individual share against the excess return of the market as a whole.
The excess return is the difference between the return and the risk-free rate, often referred to
as the risk premium. The calculation in Table 4.11 is based on ten monthly readings in order to
demonstrate the method of calculation. In practice many more readings would be taken, and
the computation would be done by computer.
Table 4.11 Calculating beta
(1)
Monthend
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Mean
Financial_BOOK_2018_new.indb 36
(2)
Excess
return on
share J
%
4
–1
7
5
–4
9
3
10
–4
7
3.6
(3)
(4)
Excess
return of
Share
market
deviation
%
(2) –3.6
(5)
(6)
(7)
Market
deviation
(3) –2.7
Covariance
(4) x (5)
Market
variance
(5)2
3
0.4
0.3
0
–4.6
–2.7
3
3.4
0.3
6
1.4
3.3
–1
–7.6
–3.7
4
5.4
1.3
3
-0.6
0.3
6
6.4
3.3
–2
–7.6
–4.7
5
3.4
2.3
2.7
0.12
12.42
1.02
4.62
28.12
7.02
–0.18
21.12
35.72
7.82
11.78
0.09
7.29
0.09
10.89
13.69
1.69
0.09
10.89
22.09
5.29
7.21
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=
covjm
m2
=
11.78
7.21
4-37
= 1.63
Table 4.11, illustrating the calculation of beta, indicates that share J has a beta of 1.63, that is,
on average, if the market index increases by 10%, the price of share J is expected to increase
by 16.3%.
The procedure illustrated in Table 4.11 is as follows:
1. Record the returns on share J for each month using Formula 3.5 adapted as follows:
Pi – P0 + D
Rj = __________
​
​
P0
where: Rj = the excess return on share J for one month
P1 = the share price at the end of the month
P0 = the share price at the beginning of the month
D = any dividend which may have been paid during the month
2.
Record the return on the market as a whole for each month using the overall market index
as the basis, as follows:
OMI1 – OMI0
____________
​
​+ OMD0
Rm =
OMI0
where: Rm= the return on the market as a whole for one month
OMI1 = the overall market index at the end of the month
OMI0 = the overall market index at the beginning of the month
OMD0 = the overall market monthly dividend yield
3.
4.
5.
6.
7.
Calculate the excess returns for both share J and the overall market by deducting the riskfree rate from the returns recorded in 1 and 2 above (columns 2 and 3).
Calculate the means for each set of excess returns and record the deviations from the
means (columns 4 and 5).
Calculate the variance for the market (m2)(column 7).
Calculate the covariance of the return of share J with the returns of the overall market
(covjm)(column 6).
Calculate the beta in accordance with Formula 4.13.
In this calculation the excess returns have been used, and dividends received on shares have
been included. There will be no significant difference in the calculated beta if dividends
are ignored and only price movements are used to calculate the share and market returns,
because of their relative stability. Ignoring dividends and using the full return rather than
the excess return is an alternative method which is used in practice.
Using Excel to determine betas
We can use Excel to determine betas. We will reorganise the data for Share J and the market
as follows in Excel.
We then highlight cells B4..K5, then click on Insert and then go to the Charts banner. Then
select the scatter chart type. Once we have the graph, click on the data points (data points
will be highlighted) and right click and then select Add Trendline. After that select the Linear
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option, and click on the Display equation on chart box and then the Display R-squared value
on chart box. This will display the equation in the form of y = bx + a, where b is the slope and
a is the intercept. In effect we are using regression analysis to determine a company’s beta. A
line that best fits the data will be inserted by Excel into the scatter graph.
It is also possible to determine the beta directly by using the SLOPE function in Excel. We
can determine R-squared (R2) by using the RSQ function and we can determine the intercept
by using the INTERCEPT function.
Cell B7 = SLOPE(B5..K5,B4..K4)
Cell B8 = INTERCEPT(B5..K5,B4..K4)
Cell B9 = RSQ(B5..K5,B4..K4)
The R-squared indicates the goodness of fit and a low R2 indicates a high level of unsystematic or diversifiable risk. The beta may be sensitive to unique events. Assume that in our
example, Share J’s excess return in October is –7% rather than +7%. This will significantly
impact on the beta which falls to 1.19 as compared to 1.63. The R2 falls to 32.4%. It is important
to analyse the underlying data and trends. Of course, in this example we are looking only
at a few data points and this effect has been accentuated. However, the principle remains
valid. Use betas with caution and apply your judgement. In the last 15 years, retailers have
experienced significant increases in share prices which may reflect consolidation in the sector
as well as favourable macro-economic factors. For periods of time, we will see movements in a
company’s share price that may be unrelated to the market due to unique or firm specific events.
For example, Vodacom’s beta in June 2010 was only – 0.12, but this may reflect underpricing
of Vodacom when it was listed on the JSE and the company experienced a subsequent upward
movement in its share price which was not related to the movement in the market, at least for a
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period of time. In the future, we would expect Vodacom’s share price to be driven increasingly
by macroeconomic factors, although the company should remain a low risk investment. The beta
for MTN was 0.86.
The beta of Vodacom was 0.62 while MTN was indicating a beta of 0.67 for the five years to
30 September 2014. The beta of MTN was 0.70 in September 2018 whilst the beta of Vodacom
was 0.74.
Let’s go back to R-squared. If a company’s beta is matched with a high R2, this will indicate
that the movements in the company’s share price are highly dependent on movements in the
market. If the beta reflects a R2 of 1, then returns are driven only by market movements and
all data points would be on the line.
A low R2 indicates that there is very little relationship between movements in a company’s
share price and movements in the overall market. To put it another way, most of the changes
in the company’s share price reflects unsystematic risk or diversifiable risk. What we cannot
diversify away is systematic risk.
Table 4.12 indicates the betas and R2 for selected firms, sectors and indices. We would
expect that sectors would depict a higher R2.
Table 4.12 Betas and the use of R-squared to measure diversifiable risk
Resources are now a much smaller part of the JSE as compared to five years ago and this has
tended to push up other sector betas over time.
APPENDIX 4.2 PERSPECTIVES: ESTIMATING THE BETA CO-EFFICIENT
Obeid Mahomed and David Bradfield offer us their perspectives on estimating beta coefficients in South Africa.
This is particularly relevant for practitioners.
Obeid Mahomed is a lecturer in Mathematical Finance, Risk Management and Financial
Technology at the African Institute of Financial Markets and Risk Management
(AIFMRM) at the University of Cape Town. His previous work experience was in the
financial services sector, with extensive exposure to banking, asset management and
brokering.
David Bradfield is an emeritus professor at the University of Cape Town and was
previously Head of Research at BNP Paribas/Cadiz Securities.
INTRODUCTION
The estimation of the beta coefficient has traditionally been achieved by running a Market Model
regression. Running this regression however can lead to a variety of practical considerations
which in turn could result in several different beta estimates. Some of these considerations could
be purely measurement-related, such as: How does one measure returns? What market proxy
should be used? How long should the return intervals be? How many data points are needed?
On the other hand, a further set of considerations involve the assumptions and the inferences,
such as: Is thin trading a problem? Is the market segmented? Are betas likely to be stable? This
appendix reviews some of the procedures that need to be considered to ensure the resulting
betas are accurate. For users of published betas, this appendix gives readers an understanding of
the care needed in the estimation of beta coefficients.
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The Market Model
The basic concept of beta arises because all stocks tend to move to some extent with movements
in the overall market. Clearly some stocks tend to move more than others when the market
moves; hence their sensitivity to movements of the overall market index is an important measure
– widely known as the beta coefficient. The Market Model has traditionally been used to estimate
the beta coefficient:
Rit = i + iRmt + eit
where
(1)
Rit is the return on asset i at time t,
Rmt is the return on the market (or benchmark) index at time t,
i and i are the intercept and slope (beta) coefficients to be estimated for asset i, and
eit is a measure of idiosyncratic asset-specific effects on asset i at time t.
The market model is commonly estimated using ordinary least squares regression (OLS). In this
instance the OLS estimate of beta is simply:
cov(Rit; Rmt)
i = __________
​​
​​
var(Rmt)
(2)
It should be noted that the market model is not based on any assumptions about investment
behaviour but simply posits a linear relationship between stock returns and the market return.
Figure 4.16 and Figure 4.17 show the scatter diagrams for the two stocks Naspers Limited and
Sun International Ltd regressed on the All Share Index (ALSI) respectively. It is evident that
the estimated (OLS) beta for Naspers Limited is 1.60 and for Sun International Ltd is 0.3227,
indicating their differing sensitivities to market movements. It should be noted that whilst this
appendix focuses on the estimation of betas on individual stocks, the concept could be applied to
any asset, including investment portfolios.
Figure 4.16 Scatter diagram for Naspers Ltd
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Figure 4.17 Scatter diagram for Sun International Ltd
Return measures
The user has two choices, either discrete or continuously compounded returns can be used, as
long as the consistency between the asset returns and the market index proxy is maintained. It
is generally accepted that returns are continuously generated through calendar time; however,
because trading occurs at discrete intervals, observers view returns as if they are generated at
discrete intervals. For both discrete and continuously compounded returns it is important to
note that the returns should be adjusted for capitalisation changes and dividends.
The Market Index
In theory, market capitalisation weighted indices are preferred to equally weighted indices
because they are superior proxies to the true market portfolio. Hence in South Africa, the
All Share Index (ALSI) should be used. It should be noted that some practitioners argue that
there is a segmentation between the Resources and Financial and Industrial sectors on the JSE
and consequently prefer to use these sub-sector indices as an overall market proxy for stocks
belonging to these sectors. It should, however, be noted that the received theory calls for an
index that is as comprehensive as possible in covering the market.
Length of the estimation period
Estimates based on many years of historical data may be of little relevance because the nature
of the business risks undertaken by companies may have changed significantly over a long period
such as 10 years. The choice of a 5-year estimation period is based on the findings that betas
tend to be reasonably stable over 5-yearly periods. The selection of a 5-year period represents
a satisfactory trade-off between a large enough sample size to enable reasonably efficient
estimation and a short enough period over which the underlying beta could be assumed to be
stable.
The return interval
Research has been directed at establishing the impact that different interval lengths have on
estimates of beta. As a consequence, subsequent researchers generally use monthly intervals
(over a 5-year period) to compute the returns needed for the estimation process, resulting in 60
data points of monthly returns.
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Correcting for the regression bias using a Bayesian adjustment
A number of studies have documented that individual stock betas have a regression tendency
towards the grand mean of betas of all stocks on the exchange. This regression bias can be
described as follows: an estimated beta coefficient which is far higher than the average beta is
more likely to be an overestimate of the true beta than an underestimate. Similarly, a very low
estimated beta is more likely to be an underestimate. Thus, the estimates of beta obtained from
the regression analysis may be suboptimal for forecasting purposes. To correct for the regression
bias, a “Bayesian” adjustment can be implemented. Hence betas can be corrected as follows:
^
​​ ​​ = wOLS + (1 – w)​¯
​
​  ​OLS(3)
2
w = ​​  _________
​​
2
2
( + OLS)
(4)
where OLS is the OLS estimate of beta
​​ ¯
​​OLS is the average OLS beta of all stocks in the market
OLS is the standard error of the OLS estimate of beta
 is the cross-sectional standard deviation of all the estimates of beta in the market
It can be readily seen from the above formulation (4) that the weight, w, assigned to the OLS beta
will be large if the cross-sectional standard deviation () is large. In other words, if the spread
of the betas across the stocks is so large as to make all values of beta equally likely, then the
OLS beta estimator is optimal. Conversely, if the standard error of the OLS beta estimate, OLS,
is large relative to , then w will be small and the Bayesian estimate of beta will be “shrunk”
towards the overall average beta of the stocks on the market. Therefore, an estimate of beta
which falls outside the usual spread of beta (and which has a large standard error) is likely to be
an overestimate. Hence the above expression corrects for the commonly observed phenomenon
that very high beta estimates that are unreliable (large standard errors) tend to be overestimates
and very low betas that are unreliable tend to be underestimates.
Adjusting for thin trading
The bias in beta estimates caused by thin trading on the JSE has been well documented. If a
stock is thinly traded then it is likely that the month-end price may not arise from a trade on that
day but may instead be recorded as the price last traded during the month. Consequently, the
recorded price on the market index at month-end may not be matched to a trade for the stock on
the day – hence a mismatch occurs. This mismatching phenomenon clearly has an impact on the
covariance estimate between the stock and the market proxy, leading to a bias in this covariance
estimate and consequently a bias in the estimate of beta.
Several researchers have derived techniques for obtaining unbiased estimates for beta in
infrequently traded environments. Two distinctly different approaches have emerged; the
“trade-to-trade” estimator and the Cohen estimators. It was found that the trade-to-trade was
superior for application on the JSE. In the trade-to-trade method the returns on the stock and
on the index are measured between the times of the last trades in successive months. Thus, a
statistical correction needs to be made for potential durations in return no longer being equal.
Furthermore, to improve the efficiency a correction is required for the heteroscedasticity in the
residual component – this leads to the final trade-to-trade estimator proposed by Dimson and
Marsh:
___
Rmt
Rit
____
​​  ___
​​ = i​​√Dit ​​ + i​____
​  ___
​​ + eit(5)
​√Dit ​
​√Dit ​
where
Dit is the proportion of a month between successive traded months for stock i and
month t.
Rit are the returns computed over the last traded day in each month.
Rmt are the market returns matched to the same consecutive traded days as stock i.
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Other issues relating to the use of betas
The stability of betas
Detection of beta stability is clouded by the fact that only the estimates of beta are observable.
Changing estimates do not necessarily imply stable underlying betas. Research indicates that the
results of tests on the stability of betas are difficult to interpret but the JSE betas were found to
be as stable as betas of stocks on the UK market.
Robust estimation of beta
Research indicates that the robustness required for estimating betas involved down-weighting
not only the outlying residual values, but also the outlying market returns.
Dynamic estimation of beta
Filtering and smoothing techniques can serve as useful aids in the interpretation of time series
of return observations. Techniques are available that categorise the movements in the levels
of stock returns as either permanent shifts in the riskiness of the firm, or as one-off events
attributable to specific circumstances.
Using a “beta book”
There are many services that supply betas and associated estimates arising from the Market
Model. We have included an extract (with the FTSE/JSE All Share Index (J203) as the Market
Index) from the Equity Risk Service (September 2018) published by AIFMRM. This is one
of the most widely used beta services in South Africa. This service uses both the trade-totrade correction procedure given in equation (5) as well as the Bayesian correction procedure
(equation (3)).
The above table represents the output from a typical beta service. The columns give statistics
emerging from market model regressions. The following interpretations are relevant:
Alpha: This is the average return (per month) on the share when the market on
average does not move.
SE Alpha/Beta: The standard error of alpha/beta is a statistical measure of the reliability of
the estimate of alpha/beta. The lower this figure, is the more reliable the estimate of alpha/beta.
Statisticians set up confidence intervals for the estimate of alpha/beta by adding and subtracting
2  SE Alpha/Beta from the alpha/beta estimate. There is a 95% chance that the true alpha/beta
lies in this interval.
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Total Risk: This is the standard deviation of returns measuring the share’s total risk expressed in
% per month.
Unique Risk (or Specific Risk): This reflects the fluctuations in the security’s returns that are
linked to events unique to the company (e.g. bad management, worker strikes, etc.).
R2: This can be interpreted as the proportion of the share’s total risk accounted for by its
market risk. Note that a high beta will not necessarily produce a high R2. In statistical terms, R2
is the coefficient of determination of the regression.
Start Date & End Date: These specify the first and last month in the period of analysis for a
specific company – this varies depending on when the respective company listed on the exchange.
% Days Traded: The number of days over the period of analysis during which the security was
traded. This provides an indication of the extent to which the security is thinly traded. In some
instances, for extremely thinly traded securities, more than 5 years of data may be needed in
order to obtain a data set that is large enough to warrant statistical estimation.
SUMMARY10
The primary aim of this appendix has been to provide guidance to the practitioner wanting to
estimate betas. Research in South Africa has indicated significant bias in beta estimates caused
by thin trading as well as the regression tendency (for betas to revert to the mean). Hence of all
the refinements briefly discussed, the most important of these are the thin-trading correction
(especially when it is known that stocks suffer from thin trading) and the Bayesian correction.
10
This appendix draws from the article On estimating the beta coefficient by D Bradfield in the Investment
Analyst Journal, No. 57, 2003, 47–52.
APPENDIX 4.3 PERSPECTIVES: BEHAVIOURAL FINANCE
Darron West (MCom MPhil LLB CA(SA) CFA) is a practising advocate,
member of the Cape Bar and a part-time senior lecturer in the Department of
Finance and Tax at the University of Cape Town. He continues to consult to
the investment management industry occasionally, and he is a non-executive
director of a South African short-term insurance company. Since his career
started in financial services in 1998, he has watched behavioural finance at
work in the South African financial markets. His experience spans derivatives,
structured investment products, fund management, venture capital, non-profit
organisations and insurance. His background in finance and his more recent
practise of the law have led him to the conclusion that EQ might well be more
important than IQ.
Classical finance theory teaches us the proverbial efficient markets hypothesis (EMH). In
a nutshell, the EMH postulates that prices on traded assets reflect all known information;
hence, such prices are unbiased. Consequently, it is impossible to consistently outperform the
market on a risk-adjusted basis except through sheer luck. Investors seek to maximise their
utility, and as such they have rational expectations (on average, but for every lunatic there is
an offsetting sane and prudent participant).
However, even a casual analysis of the price series of an equity market compared with its
rational valuation (the present value of discounted cash flows) illustrates that the unexplained
component of the efficient market models is substantial. Why is it that at the late stages of a
bull market, prices appear to be driven up without any consideration of value? Why is it that
at the end of market crashes, prices appear to be in free fall as investors exit their holdings
irrespective of value? If EMH held, surely participants should always take advantage of
fundamentally mispriced securities?
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The fact is, they don’t. The evidence suggests market overreaction is beyond the realms
of rationality. Price is not equal to the present value of discounted cash flows, risky assets are
not necessarily rated lower than riskless assets and markets are not reasonably efficient most
of the time.
The reality is that market participants are not automatons. Programme trading aside,
market participants are human beings with all the foibles and trappings of that condition. Truly
understanding the financial markets must involve an understanding of investor psychology
and the associated (and often systematic) non-rationality that follows. This does not imply
that EMH should be dismissed; rather, it connotes an attempt to have a more complete
understanding of market behaviour.
It would be trite to suggest that behavioural finance is merely the incorporation of
psychology into finance, but it certainly involves specific consideration of human and social
cognitive and emotional biases and dispositions in better understanding how and why economic
decisions are made, and how these decisions affect market prices, returns and the allocation
of resources.
A simple test will reveal a differential treatment of risk. Given a choice between (1) a
100% chance of winning R1m, and (2) an 89% chance of winning R1m, a 1% chance of
winning nothing and a 10% chance of winning R5m, most people would choose (1), even
though the rational probability weighted payoff of (2) is higher. However, when faced with a
choice between (3) an 11% chance of winning R1m and (4) a 10% chance of winning R5m,
most people would choose (4). The rational utility preference is simply not consistent, and the
cognitive impact of certainty or near-certainty is far higher than perceived remote or unlikely
events.
The experiment above is an exposition of prospect theory, coined seminally by Kahneman
and Tversky in 1979 (for which Kahneman was awarded the Nobel Prize for Economics in
2002). Prospect theory shows how human beings have a concave utility curve for gains, and
a convex utility curve for losses. More bluntly, we feel the pain of losses (even small ones)
from a reference point far more acutely than we feel the joy of gains. Many of the observed
behaviours and biases inherent in human participation in the financial markets flow from this
simple basis.
Once sensitised to them, it is hard not to observe these behavioural biases in ourselves
and in others. Most revolve around the perception and understanding of loss. Because it is
painful to make a mistake, we attempt to avoid regret by altering the basis of evaluation so as
to change an outcome from failure to ‘deferred success’. Separating actual losses from paper
losses, holding on to losing stocks and selling winners early are all symptoms. Similarly, as
the fabled (and, indeed, fictional) ostrich, we figuratively bury our heads in the sand when
confronted with new information that would challenge our beliefs or assumptions (and so
force a reversal of the action we have taken, or induce regret). This ‘cognitive dissonance’
manifests broadly, from avoiding advertisements for newly purchased products (in case they
are cheaper elsewhere), to avoidance of information about a new investment (in case it proves
to be misguided).
Research has shown how we are influenced by reference points (anchoring) in determining
outcomes, we fail to view portfolios on an aggregate basis (creating mental compartments), we
create the illusion of patterns where none exist and attribute gains to bad luck (the problem
of overconfidence), and we fit hypotheses to data instead of considering probabilities more
rationally (the representativeness heuristic).
In fields requiring some prospective estimation to justify decisions, overconfidence has
been shown to be a perennial failing. Forecasts have been shown to be both too high and hardly
useful at predicting turning points. Furthermore, studies examining gender differentials have
shown that women are less overconfident, trade less (thus incurring lower costs) and produce
better returns than men (which begs the question why the fund management industry remains
so male dominated!).
Is behavioural finance merely a tool for poking the EMH full of holes? Hardly, challenging
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the EMH is a starting point, as is using the knowledge of human behavioural biases to guard
against prejudicial or damaging financial conduct. The real power of behavioural finance has
still to be harnessed, at the very least to fill the gaps between EMH models and actual market
outcomes, and perhaps as a grand unifying theory of finance.
APPENDIX 4.4. INVESTMENT DECISION-MAKING UNDER CONDITIONS OF
UNCERTAINTY
Ameer Amod is Head of Absolute and Fixed Interest at Old Mutual Multi-Managers.
Ameer began his career in Financial Services in 2002 and has gained extensive industry
experience, working for Metropolitan Asset Managers as a Portfolio Manager,
Futuregrowth Asset Management as the Head of Quantitative Research and Peregrine
Quant Asset Management as a Quantitative Analyst. He has an MCom (Financial
Management) and an MSc (Engineering). Ameer joined Old Mutual in January 2012.
He is a published writer and regularly presents at investment conferences and to clients.
Financial markets essentially aggregate human behaviour. Cognitive biases
cause investors to produce predictable mispricing in financial markets. Research has shown that
individuals are much more sensitive to losses in wealth than to gains in wealth – in fact, twice as
much. The adage ‘crisis creates opportunity’ fails to be exploited when valuation opportunities
emerge in financial markets. Former Fed Chairman, Alan Greenspan, when referring to Black
Monday puts it succinctly ‘your judgement is less than perfect when you are scared’. We tend to
become less sensitive to valuation when things are getting bad – and when things get bad, it is
human nature to exaggerate the risks. We highlight a few useful concepts that we as students of
finance need to give due consideration when making asset allocation decisions.
TIME HORIZON
The asset allocation decision is independent of time horizon (Merton, 1969). This has always
been controversial and counterintuitive – investment advisers explicitly recommend changing the
asset mix toward more conservative investments as retirement becomes closer. At retirement,
depending on an individual’s savings to income ratio11, assets yielding 1%–2% above inflation
may not be sufficient to fund increases in future cost of living. Benartzi & Thaler (1999) have
found that retirement fund members are likely to invest more of their retirement savings in equities
rather than cash when shown longer-term rates of return. Long term should be consistent with
the length of time a member would be part of a retirement fund or some long-term savings plan.
This gives the fund member time to accumulate the higher returns generally expected from
growth asset classes like equity.
THE EQUITY RISK PREMIUM (‘ERP’)
There is an enormous discrepancy between the returns of stocks and bonds – denoted the ‘equity
risk premium’. Historically, the average return on equity has been much larger than that of
bonds. Firer & Staunton (2002) have shown this ERP to be 5.4% for South Africa over the
period spanning 1900–2001. The period 1900 to 2017 indicated a real ERP of 5.3% for South
Africa (Credit Suisse Global Investment Returns Yearbook, 2018). To quantify and interpret the
magnitude of this ERP, it is instructive to examine the US market, where we have a rich history
of data. Siegel (2014) examined the ERP for the US over the period 1802–2012 as follows:
11
Size of final retirement benefit versus the required level of income (from that benefit).
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The 2018 Credit Suisse Investment Returns Yearbook reported a real ERP of 4.4% for the USA
over the period 1900 to 2017. This reflects the strong performance of US equity markets in recent
years. The US has transitioned from an agricultural to an industrialist economy, then to the postindustrial service and technology economy it is today. Interestingly, over these transitions the
real returns from equities has been remarkably stable.
Investors today have more reason to ask what return they can expect from equities and
bonds; and what the future risk–reward trade-off is likely to be. The magnitude of the ERP
is one of the most important issues in corporate finance. It drives future returns and is a key
determinant in the cost of capital. Blanchard (1993) and Campbell & Shiller (1998) believe that
it is unreasonable to assume that the ERP will remain as large as historically observed. Siegel
(1992) explains that the higher equity risk premium is a result of the fall in bond returns rather
than a rise in the return on equity. The move away from the gold standard to paper money has
had a far greater impact on bond returns than on equities. Buyers of long-term bonds in the
1940s, 1950s and early 1960s did not anticipate the inflationary consequences of this shift in
monetary regime. It is therefore not unreasonable to believe that low real rates on bonds may
have fuelled higher equity returns supported by the low cost of leverage. The ERP is not nearly
as large as historically observed versus the post-1926 period. With many central banks targeting
inflation, holders of fixed income assets are likely to see enhanced real returns in the future –
however, equities still dominate as an asset class to long-term wealth creation.
VALUATION
Value is subjective and inherently uncertain – decisions made in most real-world applications
are in the presence of uncertainty or incomplete information. The price paid for an asset today
determines its future return. Euphoria in financial markets has led investors to pay high prices
for assets – if the future is not as rosy as contemplated by these investors, future returns will be
disappointing. Invest when expectations incorporated into asset prices are prone to extreme
pessimism; when things turn out to be ‘relatively ok’ we have the benefit of a surprise to the
upside. Howard Marks12 suggests that the action of an investor should be governed by the
relationship of an asset’s price to its intrinsic value. When assets are cheap investors should be
more aggressive in buying and conversely when assets are expensive we should exercise restraint.
Key questions to be deliberated are (i) is there a sufficient margin of safety in the current price,
and (ii) are fundamentals likely to improve or get incrementally worse?
We have discussed a few critical considerations when thinking about the asset allocation
decision. The issue of time horizon, the consideration of whether the equity risk premium is
likely to shrink in future and, most importantly, the price we are willing to pay for an asset today.
The growing area of behavioural finance has also begun to improve our understanding of the
impact of investor psychology on asset prices. We urge readers to deeply consider these issues
when making investment decisions.
12
Co-founder of Oaktree Capital Management.
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APPENDIX 4.5 PROSPECT THEORY
Dr Gizelle Willows is an Associate Professor in the College of Accounting at the
University of Cape Town and a Chartered Accountant (SA). Gizelle’s PhD was on
behavioural investing and retirement planning and she has published widely in peerreviewed journals. She has been a visiting scholar at the Haas School of Business,
University of California, Berkley. She published a column in Accountancy SA for many
years. Prior to joining UCT, Gizelle was an audit manager at PWC.
Daniel Kahneman and Amos Tversky developed a theory known as prospect theory, which shows
that as individuals, we make decisions based on the value of potential losses and gains, rather
than the outcome. Figure 4.18 helps to explain it more clearly:
Positive value
*
Less than 
Loss
More than *
Gain

Negative value
Figure 4.18 Prospect Theory
The horizontal axis measures the value of our gain or loss, whilst the vertical axis measures how
we value that gain or loss.
Looking at the horizontal line (shown as ‘γ’) on the right-hand side of the graph, it shows
the objective value of a certain gain. The vertical arrow pointing upwards reflects the subjective
value we attach to this gain. The observation to take note of is that the subjective value we place
is less than the actual objective gain.
Looking at the other horizontal arrow (measured at the same value, i.e. ‘γ*’) on the left-hand
side of the graph, it shows the same value, but this time as a loss. The vertical arrow pointing
downwards is longer than the horizontal arrow, showing that the subjective value we attach to
this loss is much larger than the actual loss itself.
If a gain or a loss, was R1 000 it shows that we place a larger value on a loss of R1 000, than
on a gain of R1 000.
Prospect theory shows us that we are loss averse i.e. risk-averse over gains and risk-seeking
over losses and centred to a set reference point or status quo. This reference point is subjective
and can be different for different people in different scenarios.
In 1974, Amos Tversky and Daniel Kahneman performed an experiment where they asked
participants: ‘what is the percentage of African nations in the UN?’ while spinning a wheel of
fortune with numbers from 1 to 100 on it. Where the wheel stopped was completely irrelevant,
however, it was found that it influenced the answers given by the participants. This study showed
how a completely irrelevant number can affect our decision-making. This behaviour is also
referred to as anchoring, a suitably named bias. Anchors of ships are put into the ocean to ensure
they don’t stray too far away from a certain point. We do the same with our reference points.
A good example of a product designed to take advantage of the behaviours attached to
prospect theory are insurance policies. If we are loss-averse and make decisions to avoid potential
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losses, then insurance products are perfect for us. They are designed to highlight the potential
loss. This then creates the anchor pushing us to choose the option that avoids such losses13.
Pain
from loss
Pleasure from gain
To summarise, prospective losses bother individuals much more than prospective gains.
Therefore, the choices we make are often based on the subjective version of a situation, rather
than the objective reality. We should be mindful of this and always differentiate between price
and value. Make decisions based on the intrinsic value of the transaction.
13
Portfolio managers will often point to capital preservation as a key part of their investing philosophy
because they understand how more important protecting capital and avoiding losses is for investors. Portfolio
allocations will include insurance type investments to avoid losses such as cash, money market investments
and bonds. Equity investments can be in such defensive sectors such as property and healthcare and high-risk
equity investments will include venture capital, biotech and mining exploration companies. Most investors will
only allocate a very small proportion of their funds to these high-risk equity investments.
Q
QUESTIONS
Question 4.1
The following summary statistics are available with regard to shares A, B and C:
■■ Expected returns:
Ra = 10%;
Rb = 13%;
Rc = 20%
■■ Standard deviations:
a = 8%;
b = 15%;
c = 25%
■■ Correlation co-efficient:
rab = 0.6;
rac = 0.8;
rbc = –0.4
Required:
(a) Determine which of shares A, B, and C would be the most attractive to a risk-averse investor
who uses the mean-variance criterion to minimise the risk per unit of return. A ranking of
shares A, B, and C is required.
(b) An investor intends to hold a portfolio of investments comprising two of the three shares
A, B and C (equal amounts would be invested in each of the two shares), therefore the
following options are available:
– Option 1: 50% in each of shares A and B
– Option 2: 50% in each of shares A and C
– Option 3: 50% in each of shares B and C
Determine which of the three options would be the most attractive to a risk-averse investor.
A ranking of the options is required.
Question 4.2
Two shares, P and Q, offer the following four historical percentage annual returns:
An investor decides to hold a portfolio of 40% invested in share P and 60% invested in share Q.
It is evident that the calculations will suffer from small sample bias. Nevertheless, you are
required to demonstrate the procedures used for the calculations and your ability to interpret
the results.
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Required:
(a) Calculate the correlation co-efficient of shares P and Q.
(b) Calculate the expected return on the portfolio.
(c) Calculate the variance of the portfolio.
(d) The investor believes that the risk of a portfolio containing any combination of P and Q will
always be less than the risk of holding either P or Q alone. Discuss whether you agree or
disagree with this view, giving reasons.
Question 4.3
An investment of R500 000 held by your company at the riskless rate of return of 8% has just
matured. It has been decided to invest the proceeds in ordinary shares listed on the JSE. Two
shares, A and B, have been identified with a correlation co-efficient between A and B (rab) of
zero, and you can invest the full R500 000 in either of them, or in a portfolio with some of each.
The following facts are available regarding the two shares:
Share AShare B
Expected return10%14%
Standard deviation of returns
10%
15%
Required:
(a) Draft a table which shows ‘expected portfolio % return’ and ‘% standard deviation of
portfolio return’, given that the five following portfolios are considered: Investment in share
A (the balance in share B) – 100%; 75%; 50%; 25%; 0%.
(b) Sketch a graph that plots the five portfolios in terms of expected risk and return. Label points
that indicate:
(i) The feasible set of portfolios.
(ii) The efficient set of portfolios.
(iii) The indifference curves of an extremely risk-averse investor, and
(iv) The indifference curves of a moderately risk-averse investor.
Question 4.4
The following limited information on annual returns is available for two shares listed on the
Johannesburg Securities Exchange.
Year
Hifli
20.1
18
Lowfli
16
20.2
22
12
20.3
36
10
20.4
12
18
Despite the limited number of readings, a normal distribution of returns may be assumed. In
addition, past performance is considered to reflect expected future performance.
Required:
(a) Calculate the average return and standard deviation of each share.
(b) Calculate the covariance of returns for a portfolio comprising shares in both Hifli and
Lowfli.
(c) Calculate the correlation co-efficient of returns in a portfolio of shares of Hifli and Lowfli.
(d) Assume you have R10 000 available to invest. If you wanted to buy either Hifli or Lowfli,
which one would you buy? Explain your conclusion.
(e) If you choose to invest R3 000 in Hifli and R7 000 in Lowfli, calculate your expected return
from the portfolio and a measure of risk.
(f) Explain briefly the rationale for investors choosing to hold portfolios of shares rather than
individual shares.
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Question 4.5
Required:
Referring to the diagram, you are required to discuss the significance of each of the following:
(f) point F
(a) curve ANMB
(b) curves 1, 2, 3
(g) point M
(c) line FC
(h) point N
(d) point A
(i) point P
(e) point B
Question 4.6
Illustrate the following with a diagram or graph, ensuring that relevant lines, points, and axes are
clearly labelled (no values need be placed on axes, and graphs need only be sketched):
(i) the probability distribution of returns on two individual shares with different expected
returns;
(ii) opportunity set of share portfolios and the capital-market line. Indicate with an L the
positioning of a leveraged portfolio;
(iii) the effect on risk of holding an increasing number of individual shares in a portfolio;
(iv) the security-market line – indicate with an R the positioning of a share with a higher-thanaverage market risk; and
(v) approximate regression lines for four shares with beta values of 3, 1, 0.4, and 20.4 respectively.
Question 4.7
Ms Lightfoot wishes to invest 50% of her savings in shares of Company A and 50% in shares of
Company B. The expected returns and standard deviations for A and B are as follows:
Company
Expected Return
Standard
Deviation of returns
A10%15%
B15%20%
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Required:
(a) What is the expected return of the portfolio?
(b) What is the variance and standard deviation of returns of the portfolio if the correlation
between the returns of A and B is:
a. +1.0
b. +0.0
c. –0.8
(c) Assume that she wishes to invest 40% in Company A and 60% in Company B. How would
this change the expected return of the portfolio? Recalculate the variance and standard
deviation of the portfolio’s returns, if the correlation of returns is zero.
Question 4.8
As an investor, Ms Malinga is considering investing in shares rather than bonds. This is due to
the recovery in equity markets. She is considering investing in the shares of three companies,
Company X (a utility), Y (a retailer) and Z (a mining company). The expected return on the
market is 12% and the risk-free rate is 7%. She wishes to use the CAPM to estimate the required
rate of return for the three shares. The beta for each share is set out as follows.
Share
X
Y
Z
Beta
0.50
0.85
1.20
What is the required return for investing in the shares of X, Y and Z?
Question 4.9
The risk free rate has just increased from 5% to 8%.
1. How would this change the intercept point of the capital market line with the efficiency
frontier?
2. How would this change the slope of the securities market line?
3. What does this say about the type of securities that would be preferred in times when interest
rates are rising?
Question 4.10
Imagine you have R200 000 to invest in a portfolio of two risky securities plus a riskless asset. The
following information contains four risky securities that are in different industries:
Required:
(a) Which two stocks did you choose and why?
(b) Given that your wealth is allocated to these two stocks plus the riskless asset in the proportions
of 15%, 45% and 40% respectively, what is your expected rand and percentage return for
your portfolio?
(c) Use the Markowitz technique to calculate the variance of this portfolio.
Question 4.11
Mr. Bhamjee places 40% of his funds in Security X which has a return of 12% and 60% of his
money in Security Y which has a return of 18%. The standard deviation on Security X is 20%
and on Y is 15% respectively.
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Required:
(a) Calculate the expected return on the portfolio.
(b) Calculate the standard deviation for the portfolio if the correlation between the stocks is
+0.5.
(c) Calculate the standard deviation for the portfolio if the correlation between the stocks is –0.5.
(d) Which of the above correlation factors is the best for the portfolio? Explain why this is so.
Question 4.12
A security analyst provides the following forecasts for the forthcoming year for an investor
seeking to invest R100 000:
State of the
economy
Probability
of state
Return of
market portfolio
Return on
Security A
Return on
government security
Strong
0.2
25%
27%8%
Moderate
0.5
15%
17%8%
Weak
0.3
5%
–3%8%
Required:
(a) Compute the expected return (mean value), standard deviation, and co-efficient of variation
for each of the following three portfolios:
(i) The entire amount of R100 000 is invested in the market portfolio.
(ii)An amount of R70 000 is invested in the market portfolio and the remaining R30 000 in
a government security.
(iii)An amount of R50 000 is borrowed at the government security rate of 8% and the full
R150 000 is invested in the market portfolio.
(b) Plot the above three portfolios on a graph depicting risk (p) and return (Rp). Please label
the relevant aspects clearly.
(c) Critically comment on the investment analysis in part (a) and part (b) above.
(d) Compute the beta for Security A and determine an appropriate return for Security A based
on its beta value.
(e) Discuss the significance of the beta value for Security A, computed in part (d) above, in
terms of risk and expected return.
Question 4.13
The capital asset pricing model provides a basis for arriving at the expected rate of return on a
security or portfolio by reference to the risk-free rate, the expected return on the market, and
the beta value of the security or portfolio. The beta value measures only a component of total
risk – that which is referred to as systematic risk.
Required:
(a) Using the capital asset pricing model, calculate the expected rate of return on a security for
which:
– the risk-free rate is 11%;
– the expected return on the market is 22%; and
– the beta value is 1.2.
(b) Give the reasoning to justify the consideration of only systematic risk in estimating the
expected return on a security.
Question 4.14
The following facts pertain to Amtel, a share listed in the industrial sector of the JSE.
Beta co-efficient
= 1.6
Expected dividend (D) = R3
Expected growth rate (g) = 5%
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In addition it is ascertained that the current risk-free rate is 12% and that the required rate of
return on shares with a beta co-efficient of 1 is 17%.
Required:
(a) At what price would you expect Amtel to be quoted today?
(b) Assuming there was an increase in the money supply which reduced the riskless rate to 10%,
at what price would you expect Amtel to be quoted?
(c) If, in addition to (b) above, the required rate of return on the market dropped to 15%, at
what price would you expect Amtel to be quoted?
(d) In addition to (b) and (c) above, assume new management of Amtel institutes policies that
increase expected growth to 7%, and expected stability in profits causes the beta co-efficient
to decline to 1.2. Determine the new equilibrium price.
(e) Discuss two factors that you consider to be significant drawbacks in effectively using the
capital asset pricing model for the valuation of shares on the JSE.
Question 4.15
You have recently been appointed as the portfolio manager of a small syndicate holding the
following shares:
Share
Investment
Share Beta
P
R800 000
1.2
Q
R400 000
1.8
R
R500 000
2.0
S
R300 000
1.4
It has been established that there is a 60% probability that the market return will be 14%.
However, should the recession deepen, the return will drop to 8%.
Required:
(a) Establish the rate of return anticipated from share R if the risk-free rate is 7%.
(b) Calculate the effect on the expected return and risk of the portfolio of the sale of shares in P
and reinvestment of the R800 000 in a new share X with a beta of 2.5.
(c) Briefly discuss what action, if any, you would take as the portfolio manager if you anticipate
an economic recession in the near future.
Question 4.16
Identify the curves or points referred to below by writing down the relevant letter(s) reflected on
the diagram set out on the following page:
(a) the efficient frontier where the investor is able neither to borrow nor to lend;
(b) the efficient frontier where the investor is able to lend at the risk-free rate but is not able to
borrow;
(c) the efficient frontier where the investor is able to lend and to borrow at the risk-free rate;
(d) the market portfolio;
(e) a portfolio where 75% of the investor’s funds are invested in the market portfolio and 25%
in risk-free securities;
(f) an example of a portfolio where the investor has borrowed to invest in the market;
(g) an example of an inefficient portfolio; and
(h) the optimal portfolio for an investor with the set of indifference curves given in the diagram
where he is able to invest in risk-free securities.
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Question 4.17
The following data are available for four shares listed on the JSE:
Share
Expected return % Expected beta
1
Jampak
17.0
1.3
2
Colder
14.5
0.8
3
Moonpak
15.5
1.1
4
Zappi
18.0
1.7
The risk-free rate is 10% and the expected return on a market portfolio is 15%.
Required:
(a) Draw a graph depicting the security-market line and plot each of the four shares.
(b) On the basis of the expectations, identify the shares which are overvalued and those which
are undervalued.
(c) If the risk-free rate were to rise to 12% and the expected return on the market portfolio to
16%, which shares, if any, would be undervalued?
(d) Assume you held a portfolio invested equally in each of the four shares under market
conditions as per (c) above. You want to invest in a fifth share, so that the portfolio beta is
1.2, and you are equally invested in five shares.
(i) What should be the beta of the fifth share?
(ii) What would be the expected return on the new portfolio?
(iii)Discuss briefly whether it would be appropriate to use beta as a measure of risk for the
new portfolio.
Question 4.18
You have been called upon to advise a client with regard to an investment of R100 000 in shares
in the industrial sector of the JSE. You have gathered data and assigned probabilities to expected
returns under four possible market conditions. The following probabilities have been assigned
to two individual shares, and to a unit trust. The unit trust is a widely diversified portfolio with
a beta of 1.
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Market condition
Probability
% Expected returns
Aruntex Boumet CD Trust
Poor
0.2
–10
10
–5
Moderate
0.3
5
10
15
Good
0.4
30
15
25
Exceptional
0.1
45
20
35
You may assume that, despite the small number of readings, the distributions all have the
characteristics of a normal distribution. In addition, you may assume that borrowing and lending
is possible at the risk-free rate of 10%.
Required:
(a) Find the expected return, standard deviation, and co-efficient of variation for each of Aruntex
and Boumet.
(b) Find the correlation co-efficient for the returns from Aruntex and Boumet.
(c) Calculate the beta of Boumet.
(d) If your client borrowed R70 000 and invested R170 000 in a certificate of deposit Trust,
calculate the expected return and total risk of the investment.
(e) If your client invested R20 000 in Aruntex and R80 000 in Boumet, calculate the expected
return and total risk of the portfolio.
(f) Identify three simplifying assumptions used in developing the capital asset pricing model.
Question 4.19
The following information gives estimated data concerning share returns:
State of the economy
Probability of each
state occurring
Rates of return if state occurs
Market
Share A
Deep recession
0.05
–20%
–30%
Mild recession
0.25
10
5
Average
0.35
15
20
Mild boom
0.20
20
25
Strong boom
0.15
25
30
In addition, it is estimated that the risk-free rate will be constant at 8%.
Required:
(a) Calculate the expected rates of return on the market and share A.
(b) Calculate the estimated beta for share A. What is the market’s estimated beta?
(c) Based on the estimated (ex ante) beta, calculate the required rate of return for share A.
Would it be more meaningful to use an ex post beta to calculate the required rate of return?
Explain your answer.
Question 4.20
Helga Mnguni has recently graduated. During her three years of study she has accumulated
savings of R10 000 and a good grasp of the theories underlying risk and return as they apply
to the JSE. She has followed three particular companies closely and has used statistical data
relating to these shares in a project. She now wishes to invest her funds into some combination
of these shares applying the principles of portfolio theory. Her data for the three companies are
as follows:
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Barloworld
Delta
Wooltru
Expected return
15%
25%
20%
Variance of return
64%
225%
81%
Beta
1.0
1.5
4-57
1.2
Correlation co-efficient
Barloworld/Delta
–0.3
Barloworld/Wooltru
+0.6
Delta/Wooltru
+0.2
Helga wishes to invest in a portfolio which comprises two of the three shares, applying R5 000 to
each of the two selected.
Required:
(a) Determine the portfolio of two shares which would be most attractive and comment on your
recommendation.
(b) Calculate the covariance of returns on the market with returns of Delta.
(c) Identify the fundamental principle of portfolio theory and the most significant assumptions
on which portfolio theory is based.
Question 4.21
Two shares record the following percentage returns based on five readings:
Required:
(a) Calculate the correlation co-efficient for shares A and B.
(b) Calculate the beta of B.
(c) Sketch the possible combinations of A and B which could be held by an investor in a risk/
return space. Label both axes and Points A and B. Indicate the following on the graph with
regard to the portfolio:
(i) Point P, where an investor who is highly risk-averse may invest.
(ii) Point Q, where an investor who is not highly risk-averse may invest.
(iii) Point R, where an investor could, but would not, invest.
(d) If the risk-free rate is 9%, and the return on the market is 11.5% sketch the securities market
line. Label both axes clearly. Indicate the following on the graph:
(i) Point X, a share with the same systematic risk as the market.
(ii) Point Y, an overpriced share.
(iii) Point Z, underpriced share.
Question 4.22
Using the letters of the alphabet given below, label the following clearly on a diagram of the
security market line where the risk-free rate is 15%:
(a) the systematic risk and the expected rate of return on the market portfolio;
(b) an example of an underpriced security;
(c) an example of an overpriced security;
(d) an example of a correctly priced security;
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(e) the systematic risk and the expected rate of return for a portfolio where 25% of the total
resources are invested in risk-free securities and 75% in the market portfolio;
(f) the expected rate of return and systematic risk for an example of a security constituting a
defensive investment; and
(g) the expected rate of return and systematic risk for an example of a security constituting an
aggressive investment.
Question 4.23
Describe the three concepts of the ‘efficient market hypothesis’ (EMH) and discuss the possible
implications of these concepts with respect to technical analysis and fundamental analysis.
Question 4.24
You are required to discuss why investors’ utility curves are important in modern portfolio theory
(MPT). Use a diagram (graph) to demonstrate your answer.
Question 4.25
Studies have indicated that a firm’s annual financial statements are an important source of
information for making equity investment decisions. Yet, other studies indicate that share prices
do not react significantly to the publication of the annual financial statements. How would you
reconcile these results with each other and with the Efficient Market Hypothesis?
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5
COMPANIES AND INVESTORS EMPLOY FINANCIAL RATIOS TO EVALUATE
PERFORMANCE
Management and investors make extensive use of financial analysis and financial ratios to
monitor and evaluate corporate performance. For the management of Clicks, the turnover of
inventory is critical for managing its business effectively and it will be monitoring its inventory
turnover ratios, the gross margin per product line and its operating margins for its divisions very
closely.
Investors are also interested in seeing whether Clicks has been able to improve or maintain its
margins and whether the company has been able to improve its operating efficiency by reducing
its inventories and operating expenses. Ratios will help investors to evaluate whether they should
invest in the company or not.
Warren Buffett is probably the world’s most famous investor. So which ratios does Buffett
look for when he is deciding to invest in a company? Buffett is focused on return on equity rather
than on earnings per share and likes to invest in companies with high profit margins. However,
the return on equity should be driven by operations and not by increasing the debt/equity ratio.
In fact, Buffett prefers companies to have low debt/equity ratios. Companies should trade at
reasonable price–earnings (P/E) ratios but he would rather discount future cash flows than
simply invest in low P/E companies or companies with high dividend yields or low price-to-book
ratios.
Financial analysis goes beyond ratio analysis. We need to evaluate whether the accounting
policies used by companies are appropriate. We need to read what the Chief Executive Officer
(CEO) and Chief Financial Officer (CFO) write in the integrated annual report and we
sometimes need to read between the lines. Furthermore, integrated reporting goes beyond just
evaluating financial indicators. We need to evaluate firm performance in terms of sustainability
and how it impacts on society and the environment.
In this chapter, we will also evaluate how we use ratios to predict company failure. We will
determine the economic value added (EVA) of a company, which will indicate whether a firm
is adding or destroying value. We will then go beyond the numbers to understand a company’s
performance and financial position and will list some warning signs of potential problems with a
company’s annual financial statements.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Outline the various reports used to communicate financial information to stakeholders.
■■ Identify the objectives of financial statement analysis.
■■ Identify the limitations of using accounting data to perform financial analysis.
■■ Outline the various approaches to financial statement analysis and to identify when each
approach is appropriate.
■■ Calculate and interpret commonly used financial ratios.
■■ Draw up a Du Pont analysis and interpret a structured financial analysis.
■■ Use failure prediction models to establish potential financial distress.
■■ Outline the limitations of ratio analysis.
■■ Calculate and interpret Economic Value Added (EVA).
■■ Identify the warning signs in regard to the quality of accounting data.
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INTRODUCTION
Any analysis of a firm by management, investors, and other interested parties, should include
an examination of the company’s annual financial statements. In terms of King IV, all listed
companies are also required to produce an integrated report.
In the first part of this chapter, we will examine the financial information that is available
in the integrated report and the annual financial statements. We will focus mainly on the
annual financial statements but will also explain the integrated reporting framework. This
analysis will be followed by a consideration of the objectives of financial analysis. In the
second part of the chapter, we will discuss and apply the techniques of financial statement
analysis such as ratio analysis, which are useful in assessing the firm’s relative risk and
profitability.
1 ANNUAL FINANCIAL STATEMENTS AND THE INTEGRATED REPORT
At the end of every financial year, the directors of each company have to produce annual
financial statements and in terms of the Companies Act (2008), are obliged to present them
to shareholders at the annual general meeting (AGM). The financial statements must, in
conformity with International Financial Reporting Standards (IFRS), fairly present the
state of the affairs of the company and the results of operations for the financial year. In
terms of the Companies Act, a company is required to include an Independent Auditor’s
report and a Director’s report within the annual financial statements.
Annual financial statements may also include reviews by the Chairman, the CEO and
may include segmental reviews, analysis and reviews by the CFO and heads of operating
divisions. When financial statements are combined with reviews, this is often called the
annual report. Therefore, the annual report contains financial information, which may
be broadly categorised into descriptive and quantitative information. The descriptive
statements, which include the chairman’s, the CEO and CFO’s reports, describe the firm’s
operating results during the past year and may discuss any new developments that will take
effect during future years.
If a company produces an integrated report, in addition to the annual financial statements,
then this will often include the reviews by the Chairman, the CEO and the CFO.
Integrated Report
In addition to the Company’s Act of 2008, listed JSE companies need to adhere to the
principles of King IV (see Chapter 1). In terms of King IV, a listed company should produce
an integrated report, in addition to the annual financial statements. An integrated report
effectively requires a company to include information about its strategy, its governance, its
risk management, its current financial performance, as well as its prospects for the future.
The integrated report should set out the company’s economic, social and environmental
impacts and should therefore include non-financial information. For example, a brewer
such as AB InBev that uses significant quantities of water (about 5 litres of water per litre of
beer) would report on how it is reducing its usage of water over time. In fact, AB InBev is a
leader in analysing and reducing its levels of water usage1. AB InBev would also be expected
to participate in initiatives to promote responsible drinking and support campaigns to
discourage users driving while under the influence of alcohol. Integrated reporting is about
understanding a company’s business model, and sustainability is a key consideration. An
integrated report should indicate how a company creates value. It should set out how the
external environment affects the company and how the company employs the resources and
AB InBev have indicated that the group has now achieved an industry-leading water usage ratio of 3.2
hectolitres of water per hectolitre of production.
1
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relationships (the Capitals) to create value. So what are the six Capitals indicated within the
Integrated Reporting Framework? The Capitals are depicted in Figure 5.1.
Figure 5.1 The use of the capitals to create and sustain value
The International Integrated Reporting Framework defines these capitals in greater detail.
Financial capital consists of financing or funds mainly obtained in the form of debt and
equity issues, as well as funding generated from operations or investments. Manufactured
capital refers to physical objects such as buildings and equipment. Intellectual capital refers
to intellectual property such as patents, copyrights, rights and licences and organisational
capital such as systems and protocols. Human capital includes people’s competencies,
capabilities and experience. Social and relationship capital refers to institutions, networks
and the relationships between stakeholders, as well as the ability to share information.
Natural capital refers to all renewable and non-renewable environmental resources such as
water, air, land, eco-systems, forests and minerals.
A company’s business model employs these capitals as inputs and converts them into
products or services. The focus is on how a company uses these capitals to create value.
With reference to the Integrated Report, the International Integrated Reporting Framework
published by the International Integrated Reporting Council (IIRC, December 2013, p. 5)
sets out its guiding principles for preparing an integrated report and the content elements
that should form the basis of an integrated report. Two important guiding principles for
the preparation of integrated reports are that the report should have a strategic focus and
future orientation and should describe its relationships with its stakeholders. These two
guiding principles are reproduced below:
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■■ Strategic focus and future orientation: An integrated report should provide insight into the organisation’s
strategy, and how it relates to the organisation’s ability to create value in the short, medium and long term,
and to its use of and effects on the capitals.
■■ Stakeholder relationships: An integrated report should provide insight into the nature and quality of the
organisation’s relationships with its key stakeholders, including how and to what extent the organisation
understands, takes into account and responds to its legitimate needs and interests.
Other guidelines refer to the connectivity of information (which, for example, refers to
dependencies and interrelatedness between factors), materiality, conciseness, reliability and
completeness, consistency and comparability. The content elements describe what should be
included in an integrated report and are reproduced below (see IIRC, December 2013, p.5):
CONTENT ELEMENTS
An integrated report includes eight content elements that are fundamentally linked to one another and are not
mutually exclusive:
■■ Organisational overview and external environment: What does the organisation do and what are the
circumstances under which it operates?
■■ Governance: How does the organisation’s governance structure support its ability to create value in the
short, medium and long term?
■■ Business model: What is the organisation’s business model?
■■ Risks and opportunities: What are the specific risks and opportunities that affect the organisation’s ability
to create value over the short, medium and long term, and how is the organisation dealing with them?
■■ Strategy and resource allocation: Where does the organisation want to go and how does it intend to get
there?
■■ Performance: To what extent has the organisation achieved its strategic objectives for the period and what
are its outcomes in terms of effects on the capitals?
■■ Outlook: What challenges and uncertainties is the organisation likely to encounter in pursuing its strategy,
and what are the potential implications for its business model and future performance?
■■ Basis of presentation: How does the organisation determine what matters to include in the integrated
report and how are such matters quantified or evaluated?
So how do we use the information provided in an integrated report to evaluate and analyse
performance? Only listed companies will tend to produce integrated reports. If you are
analysing a listed company, then it is important to evaluate a company’s integrated annual
report by evaluating its report in relation to the IIRC’s guidelines and content elements.
Does the company’s integrated report include information that clearly sets out the
company’s strategy? This means that the company not only sets out its strategic objectives
but also sets out how it aims to achieve these objectives. It is also important that the
company indicates its current position and the challenges it is currently facing and how it
plans to address these challenges in the future. Has the company indicated how it will use
the Capitals to create and sustain value? The company should report on the state of its
relationships with its stakeholders and the risks and opportunities facing the company. The
following questions may also help us to analyse a company’s integrated report:
■■ How well does the company’s integrated report reflect the guiding principles and the
content elements set out in the Framework?
■■ How does the integrated report compare with the integrated reports of other
companies in the same sector? For example, is the information consistent and
comparable? A company may report information that contradicts information by other
companies in the same sector. Are differences in performance explained by differences
in strategy?
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■■
■■
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How does the information in the integrated report compare with or support information
set out within the integrated reports of its suppliers and customers?
Is the information set out in the integrated report consistent with the information from
independent sources?
The integrated report may include both financial and non-financial information and the
company may use key performance indicators (KPIs) to set targets and report how it is
achieving or failing to achieve these benchmarks.
FROM THE REAL WORLD: TRUWORTHS’ INTEGRATED REPORT
Truworths sets out the material issues facing the company under the following headings:
• Managing the risk of fashion
• Optimising supply chain efficiency
• Managing account risk
• Managing retail presence
Truworths sets out its objectives and targets and how it has performed, as well as the challenges
encountered during the year. It refers to fashion forecasting, analysis of buying patterns,
markdowns, response to exchange rate volatility and the use of information technology.
Truworths refers to its inventory turnover ratio, adoption of a quick response fashion model,
and ensuring the diversity of its supplier base. Managing the risk of credit is important as
the company offers its customers extended credit terms and charges interest. This involves
increasing collections capacity, the adoption of new credit scorecards, credit bureau scoring,
new account opening processes, the adoption of new technologies and the management of
rising delinquency rates, as well as compliance with legislative and regulatory requirements.
In terms of the Six Capitals, Truworths reported the following in its 2018 Integrated Report:
Truworths reports on the outcomes of the Six Capitals and we set this out in Appendix 5.3.
Annual Financial Statements
The annual financial statements are required to be set out in terms of the International
Accounting Standard Presentation of Financial Statements (IAS 1). Financial statements
present the financial position and financial performance of a company. IAS 1 states that
the objective of financial statements is to provide information about the financial position,
financial performance and cash flows of an entity that is useful to a wide range of users in
making economic decisions. Financial statements answer such questions as:
■■ What are the company’s assets?
■■ What are its liabilities?
■■ How much have the shareholders contributed in equity and retained earnings?
■■ How much has been distributed to the shareholders?
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What are the company’s income and expenses, including gains and losses?
What were the cash inflows and outflows for the period under review?
A complete set of Annual Financial Statements will comprise:
■■ A Statement of Financial Position as at the end of the period (also known as a Balance
Sheet);
■■ A Statement of Comprehensive Income. This includes operating revenue and expenditure,
financing income and expenses and other comprehensive income;
■■ A Statement of Changes in Equity for the period;
■■ A Statement of Cash Flows for the period; and
■■ Notes, comprising a summary of significant Accounting Policies and other explanatory
information.
The annual financial statements collectively offer an indication of a firm’s performance and
its financial position at the end of the financial year. Comparative information is disclosed
for the previous year, along with historical summaries of key operating statistics for the past
five years or more. Table 5.1 sets out a Statement of Comprehensive Income (also termed
Statement of Profit or Loss and Other Comprehensive Income) as well as the Statement of
Changes in Equity which we will use in this chapter to evaluate the company’s performance.
The company, Typical Limited, has 500m ordinary shares in issue. Depreciation, which is
included in expenses, was R120m in 20.2
Table 5.1 Statement of Comprehensive Income and Statement of Changes in Equity
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Table 5.2 Statement of Financial Position (Balance Sheet)
The quantitative information and the descriptive information are equally important. While
the financial statements report the financial state of affairs for the past year, the information
provided in the integrated report and in the reviews by the chairman, the CEO and CFO
gives the background to the reported events, as well as indicating management’s perceptions
about the expected future prospects. Thus the quantitative information tends to be fairly
objective while the descriptive information included in the reviews is more subjective.
Analysts use the information contained in the integrated report, and annual financial
statements or the annual report to form expectations about future earnings and dividends,
and their variability.
Statement of Comprehensive Income (Statement of Profit or Loss and Other
Comprehensive Income)
A Statement of Comprehensive Income (Income Statement) summarises a firm’s income and
expenditure over a financial year. A typical Statement of Comprehensive Income (Income
Statement) is reproduced in Table 5.1.
The Statement of Comprehensive Income (Income Statement) records the income and
expenditure for the 20.1 and 20.2 financial years. Sales revenue is disclosed at the top of this
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statement. Cost of sales is deducted from the sales revenue figure to arrive at gross profit.
Various operating costs are deducted from the gross profit to give earnings before interest
and taxation. Financing costs are deducted from this, these being the interest paid on longterm and short-term liabilities. This results in profit before taxation. Profit after taxation that
is attributable to the ordinary shareholders, is available for distribution to the shareholders
through dividends. The income tax rate will reflect an effective rate that may differ from
the corporate tax rate of 28% owing to differences between accounting income and taxable
income. Typical Limited has an effective tax rate which is between 29-30%. To enhance growth,
the firm reinvests earnings of the firm that are not paid out to the shareholders in the form
of dividends. This is disclosed in the Statement of Changes in Equity, where the amount of
dividends and transfers to retained earnings are shown. The earnings and dividends, including
dividend cover, may also be reported on a per share basis. The Statement of Changes in Equity
will also disclose changes in equity due to share repurchases, the issue of shares and sharebased payment expenses.
Statement of Financial Position
While the Statement of Comprehensive Income indicates the results of operations over
a certain period, the Statement of Financial Position provides a financial “snap shot” at
a particular point in time, normally the end of the financial year. The lower half of the
Statement of Financial Position, which is reproduced in Table 5.2, shows the sources of
capital, being divided between equity and debt. The upper half reflects the employment of
capital, this being the firm’s long-term and current assets.
The shareholders’ equity comprises share capital and retained earnings. Debt comprises
long-term liabilities and current liabilities. Long-term liabilities are debt obligations with
more than one year remaining until maturity. Current liabilities are financial obligations
with less than a year remaining until maturity. While these amounts are all to be repaid
within the next financial year, they will be replaced with new current liabilities so that a
proportion of the current liabilities can be considered permanent.
In the Statement of Financial Position, the assets are listed in order of liquidity. Less
liquid assets are presented first. Assets with a useful life of more than one year are referred to
as non-current assets. Normally these assets would include plant, equipment, furniture, land,
buildings, and any other assets that have a useful life in excess of one financial period. With
extended usage these assets will deteriorate and, as a result, depreciation is provided to reflect
the decline of the assets’ useful life. The current assets or working capital of the firm consists
of assets that are normally converted into cash within one year and form part of the operating
cycle. Net working capital is current assets less current liabilities (excluding short-term interest
bearing loans and dividends payable).
Statement of Cash Flows
This statement is designed to show the cash generated from or utilised in three major areas,
operating activities, investing activities and financing activities. Although not separately
disclosed in the Statement of Comprehensive Income in Table 5.1, you have determined
that the depreciation charge included in the expenses of the company amounts to R120m
for the year. If the Statement of Cash Flows for Typical Limited is examined (Table 5.3),
it can be seen that the major generators of cash for 20.2 were the operating activities. The
major consumers of cash were investing activities and financing activities. The bottom of the
statement reconciles the increase in cash and cash equivalents with the balance at the end of
the year. This statement is particularly useful in assessing the financial health of a company.
Research studies have indicated that one of the most useful indicators of financial health is
the relationship between cash flow and total debt.
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Table 5.3 Statement of Cash Flows
2 OBJECTIVES OF FINANCIAL ANALYSIS AND STAKEHOLDERS
The overall objective of financial statement analysis is to examine a firm’s financial position
and returns in relation to risk, with a view to forecasting the firm’s future prospects. In
examining the specific objectives of users of financial statements we need to identify different
categories of users and their information requirements. Users of the integrated report and
annual financial statements will include stakeholders such as shareholders, management,
employees, suppliers, customers, and credit granters and lenders, government and society.
Shareholders
Shareholders are the suppliers of a firm’s equity risk capital. This capital is exposed to all the
risks of ownership and provides a cover for the debt that has a preferential claim to income
and capital on liquidation. Normally this risk capital will receive returns in the form of
dividends only after the prior claims of debt for interest have been satisfied. On liquidation,
ordinary shareholders have a claim to what remains only after the prior claims of creditors
and preferred shareholders have been met.
As a result, the informational needs of equity investors are among the most demanding
of all users of financial information. Their interest would lie in all aspects and stages of
operations, profitability, liquidity, capital structure, and valuation.
Credit grantors
Credit grantors provide firms with loan capital in various forms and for a variety of purposes.
This may take the form of short-term or long-term credit.
Trade creditors who supply goods or provide services on credit normally provide shortterm credit. Most trade credit ranges from 30 to 90 days with cash discounts occasionally
allowed for specified earlier payment. Normally the trade creditor does not receive interest
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for the extended credit, the reward being the profit that flows from trading. Short-term
credit is also provided by the commercial banks. This type of credit takes the form of bank
overdrafts or term loans, and interest is payable on the outstanding balance.
Long-term credit is usually provided by commercial banks or by financial institutions in
the form of long-term loans. These loans may be secured or unsecured. Firms can also obtain
long-term funds through the sale of debentures or non-participating preference shares.
A significant characteristic of all credit extension relationships is the fixed nature of
the reward accruing to the credit grantor. If a firm should be highly profitable, the credit
grantor’s return will be limited to the agreed rate of interest. However, should the firm
incur losses, the credit grantor could lose his income if the firm stops paying interest and,
moreover, he might not recover his capital. This downside risk/return relationship has
a major impact on the credit grantor’s point of view and will influence his objectives in
conducting a financial analysis.
While the equity investor is interested primarily in future earnings and the variability of
these earnings (as these factors will determine future returns), the credit grantor, on the
other hand, is concerned primarily with specific security provisions and cash flow forecasts.
Examples are the market value of assets pledged, the existence of other resources, and the
projection of sufficient future cash flows to enable the repayment of principal and interest.
In the case of short-term credit, the credit grantor is concerned primarily with the present
financial condition and the liquidity of the firm, the type of current assets, and the rate of their
turnover. The evaluation of long-term loans requires a far more detailed and forward-looking
analysis. Future profitability in the long term and cash flow analysis would indicate the firm’s
ability to meet the interest charges arising from its debt as well as other operating commitments.
Both long-term and short-term credit grantors would also be concerned with the firm’s
capital structure. The level of financial leverage determines the level of financial risk and
indicates the extent that debt is covered by assets. The relationship of equity capital to debt is
an indicator of the adequacy of equity capital and of the cushion against loss that it provides.
Management
Management would use financial analysis to assist them in exercising control and in viewing
the firm in the way that outsiders, such as creditors and investors see it. This perspective
helps management to identify actions that will maximise shareholder wealth and ensure that
the firm receives an optimal allocation of capital resources.
Financial analysis can be undertaken by management on a detailed and continuous
basis, as management has unlimited access to accounting and other financial information.
Structured financial analysis is particularly useful in exercising control. An evaluation
provides valuable clues as to important changes in underlying financial operating conditions
as the analysis makes use of numerous relationships and interrelationships among financial
variables occurring within the firm. Identification of such changes, and a quick response to
rectify underlying problems, form the essence of control.
Employees
In order to negotiate for improved wages and benefits, employees and unions need to study
the annual report of the firm to find the relationship between profitability and the amounts
paid to employees. Employees may also be interested in the long-term viability of the firm
since this has a bearing on future job security. In this regard their interests would be similar
to those of long-term credit grantors – the future long-term profitability of the firm.
Customers
Customers may wish to analyse the financial statements in order to ensure the future reliability
of supplies and the value of warranties. If the company provides warranties and spare parts,
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then customers will want to ensure that the company is financially secure and has a sustainable
business model in the longer term. Furthermore, customers can also use information from the
financial statements to negotiate improved prices if the financial performance and financial
position of the company indicates that the company is financially secure.
Suppliers
The company’s suppliers will analyse the integrated report and annual financial statements in
order to evaluate the company’s profitability and financial position so that the suppliers can
continue to sell to the company and to ensure that any trade credit provided to the company is
secure. Suppliers will monitor the company’s liquidity and ability to pay its short-term debts.
It is also important for a company to analyse the financial statements of its suppliers to ensure
the reliability of the supply of goods.
Acquisition and merger analysts
In identifying possible acquisition or merger candidates, analysts attempt to determine
an economic value for a firm as a whole. The analysis of financial statements helps in the
determination of an economic value and in assessing the potential synergistic benefits.
Thus the objectives of the acquisition and merger analyst are similar to those of the equity
investor, except that in the analysis of an acquisition one must, in addition, stress test the
valuation of assets, including intangible assets such as goodwill, patents, and any liabilities
transferred.
Auditors
An auditor is called upon to express an opinion on the fairness of the presentation of financial
statements. The major purpose of the audit process is to obtain the greatest possible degree
of confidence about the absence of material errors and irregularities that, if undetected,
would affect the fairness of presentation. As material errors or irregularities would affect
the various financial, operating, and structural relationships, the use of financial statement
analysis could lead to the detection of such errors and irregularities. Further, the process
of financial analysis requires the auditor to have a deep understanding and grasp of the
audited firm and this overview will help to indicate the most relevant type of audit work. If
the financial statement analysis is conducted at the end of an audit, the analysis will provide
an overall indication as to the reasonableness of the financial statements in general.
Government
Financial statement analysis may serve the needs of government departments. For example,
SARS could use financial statement analysis to check the reasonableness of income tax
returns and payment of indirect taxes such as VAT.
3 LIMITATIONS OF ACCOUNTING DATA
Financial statement analysis is dependent upon accounting data. While the importance of
accounting data in financial decision-making should not be understated, there are certain
limitations. If these limitations are considered, the correct perspective can be applied to the
analysis. The major limitations of accounting data are as follows.
Monetary expression
Accounting data contains information that can be expressed in terms of monetary value.
Hence any attribute that cannot be expressed in terms of rand value would tend to be
ignored. For example, the Statement of Financial Position of Typical Limited lists the rand
value of all the assets, yet one of the company’s most important attributes is its management
team. The accounting data makes no effort to value these human resources. Likewise there
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could be some negative aspects that are not reflected by the accounting data. This also
makes it imperative that we study the integrated report and the reviews by management to
understand what is behind the numbers. It is also important that we study the notes to the
annual financial statements.
Simplification and summarisation
As accounting tries to record highly complex and diverse economic events, there is often
a need for simplification and summarisation. The simplification process is necessary in
order to classify the numerous types of transactions into a limited number of accounting
categories. This will inevitably result in a loss of some clarity and detail that may have
been useful. Likewise, in the financial statements, it is necessary to summarise the account
categories to keep the size and detail within reasonable bounds.
Flexible accounting policies
A proportion of the financial data contained in financial statements is based on subjective
and flexible criteria, rather than objective criteria. The subjectivity arises from the estimation
and judgement of the accountants who prepare the financial statements. If different
accounting policies are used, the financial statements of different firms may not be uniform
or comparable. For example, it is necessary to decide on a depreciation policy based on
estimates of the expected future life of assets and their residual values.
The capitalisation or expensing of research and development costs is another area
providing management with flexibility.
Inflation
Inflation leads to a decline in the purchasing power and so reduces the standard of value of
the currency. These changes are not necessarily reflected in accounting data. For example,
when measuring returns, care must be taken when comparing current income against assets
purchased twenty years ago. Reported returns will be overstated due to low historic cost
carrying values of assets and low depreciation. Current values may be much higher and yet
balance sheet values may be based on historic costs.
4 APPROACHES TO FINANCIAL STATEMENT ANALYSIS
The analyst has a variety of techniques available for analysing financial statements and can
choose the technique best suited to a specific purpose. Among the more common analytical
techniques are:
■■ comparative financial statements and trend analysis;
■■ index analysis;
■■ common size analysis; and
■■ ratio analysis.
Comparative financial statements
The comparison of financial statements is accomplished by setting up Statements of
Financial Position, Statements of Comprehensive Income, or Statements of Cash Flows
side-by-side and reviewing the changes that have occurred from year to year. The most
important factor revealed by comparative financial statements is the trend. The trend
will indicate the direction of change, the rate of change, and the amount of the change.
A meaningful trend can be established only if financial information is available for
a number of years. Normally the minimum would be five years and the ideal would
probably be ten years. This information is important for analysts as it helps them to
project future results.
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Index analysis
Index analysis is similar to comparative financial statements except that a base year is chosen
and all values for that year are expressed as 100%. Subsequent years are then expressed in
terms of percentages calculated on the base year. For example if, in the base year, accounts
receivable amounted to R80m and in the following year they amounted to R120m, the
index analysis would express accounts receivable as 100% in the base year and 150% in the
following year. Let’s apply index analysis to Typical Ltd.
Although sales revenue has grown significantly by 54% over the year, the increase
in cost of sales and expenses has been much more dramatic resulting in a fall in profit
before interest and tax. Management would wish to investigate the reasons for this and to
investigate which corrective measures the company can implement in the future. Perhaps,
the firm has focused on growing sales at the expense of profitability.
Table 5.4 Indexed Statement of Comprehensive Income
Table 5.5 Indexed Statement of Financial Position
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Common size analysis
It is often useful to show individual items as a proportion of the total group. In a common
size Statements of Financial Position, each item is expressed as a percentage of total assets.
In the common size Statement of Comprehensive Income, sales revenue is expressed as
100% and every other item is expressed as a percentage of sales revenue.
Table 5.6 Common size Statement of Comprehensive Income
A common size analysis enables us to monitor changes and trends in margins and costs. The
company has seen a reduction in the gross profit margin. It is useful to evaluate this over a
number of years to see whether this reflects a trend towards a lower level of profitability in
the future. For example, the fall in gross profit margin may reflect an increased competitive
environment or the entrance of new competitors or a fall in the prices of substitute products.
Otherwise, suppliers may have the power to raise prices and the company has been unable to
pass these cost increases to its own customers. The fall in net margin is greater as distribution
and selling expenses as well as administration and other expenses have grown to reflect a
greater proportion of sales revenue.
Table 5.7 Common size Statement of Financial Position
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Ratio analysis
A ratio expresses the relationship between one quantity and another. The ratio of 80
to 100 is expressed as 0.8:1, 0.8 or 80%. While the computation of ratios is simple, the
interpretation tends to be more complex. In examining the computation and interpretation
of a few frequently used ratios, it must be stressed that there is an infinite number of ratios
available. Many of these may be insignificant, for to be significant the ratio must express a
relationship that is meaningful. This would be reflected by a clear, direct, and understandable
relationship between the two variables. For example, sales turnover and the cost of goods
sold would display such a relationship, while on the other hand we would not expect a
relationship to exist between selling costs and the amount invested in fixed assets.
Since ratios are used by analysts to make projections about the future, the analyst should
also understand the factors that will affect such ratios in the future.
5 APPLICATION OF RATIO ANALYSIS
A ratio contains little meaningful information on its own. For a ratio to be effectively
interpreted, it needs to be either compared with historic ratios to identify trends, or with
industry ratios, or with management’s goals and standards, and it must be evaluated in the
context of associated ratios.
When comparing a firm’s ratio to industry ratios, care must be taken to ensure that the
firm itself does not unduly bias the industry ratios and that the comparison of financial data is
appropriate. As industry ratios are the mean ratios for a large number of firms, it is possible
that the individual ratios vary extensively. This would result in the industry ratios being less
meaningful.
Ratios may be categorised into six groups: liquidity ratios, asset management ratios, debt
management ratios, profitability ratios, cash flow ratios, and market value ratios. Each of
these categories will be discussed and illustrated using Typical Limited’s financial statements
as an example.
Liquidity ratios
A major concern of any analyst is whether the firm will be able to meet its maturing financial
obligations. A full liquidity analysis requires the preparation of a cash budget as described in
Chapter 12. However, by examining the Statement of Cash Flows and the amount of cash on
hand and other current assets in relation to the maturing financial obligations, ratio analysis
indicates a measure of liquidity. The two best known measures of liquidity are the current
ratio and the quick ratio.
Current ratio. The current ratio is calculated by dividing current assets by current liabilities.
Current assets normally include cash, accounts receivable, and inventory, while current
liabilities consist of accounts payable and accrued expenses. This ratio indicates the extent
to which the claims of short-term creditors are covered by assets that can be translated into
cash in the short term. The calculation of the current ratio for Typical Limited at year end
20.2 is shown below:
current assets
208 ​ = 1.73:1 (20.1 = 1.83:1)
_______________
____
Current ratio = ​
​= ​
120
current liabilities
As a rule of thumb, the current ratio should be in the region of 2:1. Typical Limited has a
current ratio which is close to this benchmark although it has decreased from 20.1. This is
caused by a greater increase in accounts payable and short-term borrowings than in accounts
receivable, cash and inventory.
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FINANCIAL MANAGEMENT
Quick ratio. As it normally takes longer to translate inventory into cash, it is useful to measure
the firm’s ability to pay off short-term obligations without relying on the sale of inventory.
The quick ratio, or acid test ratio, is calculated by deducting inventory from current assets
and dividing the remainder by current liabilities. The quick ratio for Typical Limited is:
current assets – inventory
65 = 1.19:1 (20.1 = 1.23:1)
______________________
​ = ________
​ 208 –  ​
Quick ratio = ​
120
current liabilities
The rule of thumb for the quick ratio is 1:1. Typical Limited has a ratio that is above this
benchmark. The ratio is declining as a result of the firm having relatively less accounts
receivable and cash resources in comparison to current liabilities.
FROM THE REAL WORLD: THE CURRENT RATIO
Pioneer Foods experienced a fall in its current ratio in 2017 to 1.68 from 1.96 in the previous year.
At the same time its quick ratio fell from 1.00 to 0.75. It was a challenging year. Sales declined
and operating profit fell from R2.34bn to R1.1bn. The lower current ratio and quick ratios were
mainly due to a fall in the cash holdings of the group, as well as falling receivables and inventory,
whilst trade payables rose. Tiger Brands, which operates in a similar industry, reported a current
ratio of 1.80 in its 2018 interim accounts which rose from 1.75 in the previous year. The quick ratio
was at 0.99 as compared to 0.91 in the previous year.
Distell is required to hold significant inventories and its current ratio was 2.65 in 2018 whilst
its quick ratio was only 0.99. In 2017, Sasol had a current ratio of 1.7 whilst its prior year’s current
ratio was at 2.6. Sasol’s quick ratio fell from 2.0 down to 1.2. Why did these ratios change so
much for Sasol? This was due to cash balances falling from about R50bn to R27.6bn and shortterm debt increasing from R2bn to R9.7bn. As these changes relate mainly to the acquisition of
long-term assets, we need to rather analyse the components of working capital that relates to
inventory, trade receivables and trade payables. If we just focus on operating working capital,
then Sasol’s current ratio is 1.39 as compared to 1.48 in the prior year and its quick ratio is
0.77 as compared to 0.86 in the prior year. Does this mean that Sasol is poorly managed and
may experience potential liquidity problems? Not really. Over the last 15 years, companies have
increasingly focused on reducing their net investment in working capital by using methods such as
just-in-time and advances in technology. The average current ratio per sector is often lower than
two. Current ratios that are between 1.00 and 1.80 are becoming the norm. Furthermore, service
companies will tend to have low inventories which will reduce the current ratio.
Asset management ratios
This group of ratios is designed to measure how effectively management is utilising the
company’s assets. In particular, the asset management ratios seek to ascertain whether the
investment in assets is justified in relation to activity as measured by sales revenue.
Inventory turnover. The inventory turnover ratio is defined as sales divided by inventory.
As sales are recorded at selling price and inventory is recorded at cost price, it is more
meaningful to calculate the ratio by dividing the cost of sales by inventory. The inventory
turnover ratio for Typical Limited is:
2 036
cost of sales
​ = ​ _____
​= 31.3 times (20.1 = 20.1 times)
Inventory turnover = ​ ___________
inventory
65
The inventory turnover ratio is very high and, when compared against its 20.1 ratio, shows
a significant increase. Excessive inventories are unproductive and represent an investment
with a low or zero rate of return. The increased inventory turnover ratio would also tend to
indicate that there was no build-up of damaged or obsolete inventory.
It should be noted that the inventory level used for the ratio is the inventory held at a point in
time, this being the year-end. However, in reality, most firms’ inventory levels would be seasonal
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5-17
and thus it would make sense to use average inventory levels rather than the year-end inventory
level. The sum of the opening and closing inventory levels divided by two is not necessarily the
average inventory level as no allowance has been made for volatility or seasonality during the
year. Further, for the sake of comparability, it is necessary to calculate the firm’s ratio in the
same manner as the industry ratio.
If cost of sales is not disclosed or the industry and comparative ratios are based on sales,
then we would determine the inventory turnover ratio by dividing sales by inventory. Also
we may wish to be able to reconcile all our ratios to a common base. However, this does
result in an overstatement of the true inventory turnover and is problematic if there is a
change in a company’s gross margin. In relation to working capital, another ratio is:
Sales/net operating working capital
This is essentially sales divided by (inventory + receivables – payables) and indicates the
extent of financing provided by suppliers as well as the efficiency of managing a company’s
working capital.
Average collection period (days sales outstanding, DSO). The average collection period (DSO)
represents the average length of time that a firm must wait after making a sale before
receiving the cash. The average collection period which is used to analyse the accounts
receivable is calculated by dividing average daily sales into accounts receivable to find the
number of days’ sales tied up in receivables. Where a firm sells for cash and on credit, only
credit sales should be used if a detailed split in sales is available.
receivable
122  ​ = 12.46 days (20.1 = 16.99 days)
​ = ​ _________
Average collection = _________________
​ accounts
3 573/365
sales/365
The collection period of just under 13 days is well below that of most companies. This ratio
indicates that the credit period extended by Typical Limited is very low.
This ratio can be compared with the terms on which the firm sells its goods. For example,
Typical Limited could sell both for cash and on credit. If half the sales were for cash and the
other half on credit with terms calling for payment within 30 days, the average collection
period should be 15 days. As the actual average collection period is less, it would indicate
that customers were, on average, keeping to the credit policy. On the other hand, an average
collection period that was above 15 days would indicate that, on average, customers were
not keeping to the credit policy but there could still be some customers who were. Any
customers exceeding the credit terms could be identified through the use of an ageing
analysis. Management would also be concerned if the credit policy was too tight, as this
could have the effect of reducing credit sales.
FROM THE REAL WORLD: INVENTORY TURNOVER AND DAYS SALES
OUTSTANDING
In 2018, Shoprite had an inventory turnover (COS/Average inventory) of 6.2 times whilst Tiger
Brands had an inventory turnover of only 4.0 times. This reflects the differing nature of operations
of the two firms. Tiger Brands is involved in the manufacture of food products whilst Shoprite is
mainly involved in the retailing of food. Truworths indicated a group inventory turnover ratio of
3.5 to 4.5 times and the group inventory turnover was 4.0 times in 2018. This includes the Office
UK division. The Truworths division has a higher target inventory turnover of 4.5 to 5.5 times
and the Truworths division achieved an inventory turnover of 4.8 times. Yet if we go back to 2013,
Truworths was achieving an inventory turnover of 5.4 times. Truworths acknowledges problems
in the supply chain, particularly in relation to congestion at its distribution centres.
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FINANCIAL MANAGEMENT
Tiger Brands had an average collection period (DSO) of 53 days in 2017. Days sales outstanding
(DSO) for Truworths was 98 days in 2018. This reflects its business model, which is based on
granting its customers extended credit and charging interest. Furthermore, if we only include
account sales, which make up about 69% of sales, then the DSO rises to 148 days.
Fixed asset (non-current asset) turnover. The fixed asset turnover ratio indicates the utilisation
of property, plant, machinery, and equipment relative to operating levels as reflected by
sales revenue. The fixed asset turnover ratio is:
3 573 ​ = 2.91 times (20.1 = 2.04 times)
sales  ​ = ​ _____
Fixed asset turnover = ​ __________
fixed assets 1 227
The ratio of 2.91 times compares favourably with that of the previous year (2.04 times)
indicating that Typical Limited is generating a higher level of sales from its fixed assets than
it had done in the past.
Asset turnover. This ratio measures the utilisation of all the firm’s operating assets in relation
to sales revenue and is calculated as follows:
3 573  ​= 2.49 times (20.1 = 1.76 times)
sales
___________
Asset turnover = ​ ______________
​ = ​
operating assets 1 227 + 208
If we determine the asset turnover on the basis of Sales/(PPE + NWC), i.e. sales relative
to property, plant and equipment and net working capital (which is current assets less trade
payables), then the asset turnover would be 2.67 [3573/(1227 + 208 – 98] and the comparable
20.1 ratio would be 1.88.
The total asset turnover has improved considerably. The increase in turnover is greater
than the increase in assets required to generate sales. This would indicate more efficient
asset management relative to the level of operations.
As sales are over the year, it may be more useful to divide sales by average net assets
(non-current assets plus net working capital). For example, assume that a company with sales
of R200m and net assets of R100m increases its net assets by a further R100m halfway during
the financial year. Assume that the investment in net assets will also generate sales of R200m
per year. At year end, the net assets will have doubled to R200m but sales only include sales
revenue for the second half of the year (200 + 0.5 × 200). So, if we use year end net asset
values, then it seems that the company has reduced its asset turnover from 2 to 1.5 (300/200).
Does this mean that the company has become less efficient in managing its assets? No, it is
simply that we have 100% of the new assets but only 50% of the revenue from these assets.
If we average the net assets, we obtain an average value of net assets of R150m
[(200 + 100)/2] and the asset turnover will then be 2, which is the same as the prior year.
Of course, matching asset acquisitions and revenue is not always easy if acquired at different
points in time during the year.
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Tiger Brands reported its asset turnover as follows:
Whilst Tiger Brands’ utilisation of its assets reflected a worrying trend until 2014, the group has
been able to improve its asset utilisation in recent years.
Debt management ratios
Debt management plays an important role in financial management and the extent of
financial leverage of the firm has a number of implications. Firstly, the more financial
leverage the firm has, the higher its financial risk will be. As debt finance incurs interest,
a fixed cost, earnings become more volatile with debt finance. However, additional risk
yields additional return and if the firm earns more on the borrowed funds than it pays
in interest, the return on owners’ equity is magnified. Finally, by raising funds through
debt, the shareholders can obtain finance without losing control of the firm.
It can thus be seen from the above that there are basically two aspects to financial
leverage: firstly, a change in financial risk and, secondly, some implications for the returns
attributable to shareholders. The debt management ratios will try to assess the impact of
financial leverage on risk while the profitability ratios will indicate the impact of financial
leverage on risk and shareholders’ returns.
Debt ratio. The debt ratio is the ratio of total debt to total assets and measures the percentage
of total funds provided by creditors. Total debt would include current liabilities and, in most
instances, preference shares. The higher the debt ratio, the higher the financial risk and,
while a very high ratio might be unattractive because of the high level of risk, a very low
ratio would also be unattractive because of the leveraged returns foregone. The debt ratio
for Typical Limited is:
400 + 120  ​= 36.24% (20.1 = 36.36%)
debt  ​ = ​ ___________
Debt ratio = ​ __________
total assets 1 227 + 208
The ratio indicates that just over one third of assets are funded by debt. The debt ratio has
strengthened marginally on the 20.1 ratio. This would indicate that Typical Limited has
moderate financial risk2. However, it is important to note that financial risk is the measure
of variability of returns caused by fluctuating earnings and fixed-interest repayments. Hence
it is necessary to examine interest charges and earnings before a complete assessment can
be made of the financial risk.
Debt to equity. The debt-to-equity ratio is similar to the debt ratio except that it measures the
ratio of interest-bearing debt to total equity. The ratio is as follows:
interest-bearing debt
22 = 46.1% (20.1 = 46.7%)
__________
​ = _________
​ 400 +  ​
Debt to equity =
​
915
total equity
This ratio indicates the extent that interest-bearing debt is covered by shareholders’ funds.
This ratio is consistent with the interest cover ratio.
If the debt ratio is defined as interest-bearing debt to capital employed, then the debt ratio would be 31.6%
[(400+22)/(1435–98)]
2
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FINANCIAL MANAGEMENT
FROM THE REAL WORLD: DEBT TO EQUITY
Studies have indicated that most South African companies have debt to equity ratios that are
below 40%. Therefore, what happened to PPC Cement is particularly interesting in relation to its
debt/equity ratio over time. The following depicts the debt to equity ratios of PPC in relation to
the book value of equity as well as the market value of equity (essentially its market capitalisation).
In 2005, PPC had a debt to equity book value of 23% and this rose to 66% by 2007 and 107%
by 2008 before increasing further to 409% by 2011. PPC was taking on debt to buy back its own
shares. We cover share repurchases in Chapter 16. However, the debt to the market value of
equity was still low at 25%. However, the share price and the market value of equity crashed from
about R18bn in 2012 to R6.5bn in 2016. The group experienced very difficult operating conditions
which was aligned to a falling asset (PPE) turnover ratio that was 3.19 in 2005, 1.59 in 2011 and
0.78 in 2016 before recovering a little to 0.9 by 2018. This is where debt becomes extremely risky.
There are also loan covenants which the group would struggle to meet so that PPC had to make
an equity rights issue of R4bn in 2017 in order to pay off debt so that its debt to equity ratio could
again be within a reasonable range. It also did mean that PPC, which had been buying back shares
at around R30 per share, was now issuing shares at R4 per share.
The debt to equity ratios of companies such as Bidvest, retailers and airlines may see a
significant increase in the reported debt/equity ratios due to the capitalisation of all leases from
2019 in terms of IFRS16.
Debt to EBITDA. The Debt/EBITDA ratio represents interest-bearing debt divided by earnings
before interest, tax, depreciation and amortisation.
Debt/EBITDA = (400+22)/(282+120) = 1.05
This ratio is an indicator of a company’s ability to repay its debt and measures the number of
years it will take for the company to repay its debt. EBITDA is closer to cash flow than net
profit. In this case, we used only interest-bearing debt rather than total liabilities. Lenders and
credit rating agencies will often use this ratio to indicate the probability of the firm defaulting.
PPC’s debt/EBITDA ratio rose from 1.91 in 2013 to 5.98 in 2016, indicating a much higher
probability of default. PPC was required to issue new equity of R4bn in order to bring its debt/
EBITDA ratio down to 2.49 in 2018.
Times interest earned (interest cover). The times interest earned ratio is determined by
dividing earnings before interest and taxes by the interest charge. This ratio measures the
extent to which earnings can decline without causing financial losses to the firm and creating
an inability to meet the interest cost. Failure to meet this obligation could lead to legal
action and ultimately insolvency. It should be noted that the before-tax profit figure is used
as the numerator, as income taxes are computed after the interest expense is deducted. The
times interest earned for Typical Limited is:
EBIT  ​ = ____
​ 282 ​ ​ = 2.82 times (20.1 = 5.23 times)
Times interest earned = ​ _______
100
interest
This ratio reflects a high interest charge in relation to profitability. Further, there is a
considerable deterioration of this ratio from 20.1 to 20.2. This reflects the increased longterm borrowing in 20.2 and increased interest rates. In addition, the short-term debt has
increased proportionately more than the long-term debt. The high interest cost may indicate
that borrowing levels are higher during the year than at year end.
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EBITDA interest cover. Operating income (EBIT) is after depreciation and amortisation,
which are non-cash flow charges. Therefore, it may be more relevant to determine the degree
that interest payments are covered by a figure that is closer to cash flow from operations
rather than analysing only earnings coverage.
EBIT + depreciation + amortisation
​
​
EBITDA interest cover = ________________________________
Interest
Bidvest computed an EBITDA to interest ratio of 8 in 2018 which is in line with its target ratio.
PPC reported a much lower EBITDA to interest ratio of 2.79 in 2018.
There are a number of other coverage ratios that we could compute. For example, we may
wish to determine the following fixed charge coverage ratio:
EBIT + depreciation + amortisation + lease expense
​
Fixed charge coverage = ________________________________________________
​
Interest + lease expense
The fixed charge coverage for Bidvest is 3.95 which is much lower than the EBITDA interest
cover of 8 mainly due to the fact that Bidvest reported operating lease charges totaling
R1.5 billion in 2017. From 2019, in terms of IFRS16, lease expenses will mostly fall away but
interest and depreciation will rise.
Profitability ratios
The ratios previously examined have tended to measure management efficiency and risk. As
profitability is the result of a large number of policies and decisions, the profitability ratios
will show the combined effect of liquidity, asset management, and debt management on
operating results.
Gross profit margin on sales. The gross profit margin on sales ratio is computed by dividing
gross profit by sales revenue. If we apply this to Typical Limited we get the following:
gross profit _____
​ = ​ 1 537 ​= 43.0% (20.1 = 48.0%)
Gross profit margin = __________
​
3 573
sales
The gross profit margin has declined and this could indicate that markups have been reduced
in order to increase sales revenue. If the reduction is not part of a management strategy,
the decline in this ratio could also reflect a weakening in inventory control and possible
inventory losses as well as increased competition.
Net operating profit margin on sales. The net operating profit margin on sales ratio is
computed by dividing net income before interest and tax by sales revenue. If we apply this
to Typical Limited we get the following:
EBIT ​ = _____
​  282  ​= 7.89% (20.1 = 18.02%)
Net operating profit margin = ​ _____
3 573
Sales
The net operating profit margin is fairly low and it has dropped considerably from 20.1.
This could be the result of higher costs, lower markups or a combination of these factors.
Companies are increasingly reporting EBITDA and the EBITDA margins.
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The net profit margin after interest and tax can be determined as follows:
Net profit
​
​
Net profit margin = _________
Sales
Another indicator of profitability is based on the ratio of earnings before interest,
depreciation and amortisation (EBITDA) to sales. For Typical Ltd, its EBITDA margin
would be determined as follows:
282 + 120
EBITDA margin = _________
​ EBITDA
​ = ​ _________
​= 11.3%
3 573
sales
A company such as MTN will often refer to its EBITDA margin, which was 43.1% in 2013 but fell
to 34% in 2017. Although the EBITDA margin can be useful, it may often overstate the returns
of capital-intensive firms. A company may have a high depreciation charge due to the fact that
it has a high level of investment in property, plant and equipment. Although depreciation and
amortisation are non-cash flow expenses, it will offer some indication of the capital expenditure
required to maintain operations in the future. However, banks often use EBITDA to determine
how much a company is able to borrow. For companies that are not required to undertake
any material capital expenditure in the future, this may be a useful indicator of debt capacity.
However, in most cases, it is not a good indicator of cash flow as it ignores capital expenditure
and investment in working capital. Furthermore, interest and tax are relevant expenses. Warren
Buffett does not like EBITDA. As he states: “We’ll never buy a company when the managers talk
about EBITDA”. He states more colourfully, “Does management think the tooth fairy pays for
capital expenditure?”
The following depicts the gross profit margins, operating margins and net profit margins of
Shoprite and Tiger Brands in 2017, 2013 and 2009.
Tiger Brands makes and owns products such as Jungle Oats, All Gold, Koo, Fatti’s & Moni’s, Black
Cat, Tastic, Beacon, Albany, Renown, Enterprise, Energade, Oros, Ingrams, Doom, and Jeyes.
Shoprite has been able to grow its gross profit margin over time but its operating margin did slip
slightly in 2017. Tiger Brands experienced a decline in gross profit margin, operating margin and
net profit from 2009 to 2013 but experienced a recovery in margins from 2013 to 2017.
Bidvest reported an operating margin of 8.4% in 2017. In contrast, Kumba Iron Ore earned
an operating profit margin of 46% in 2017.
Return on assets (ROA). The return on assets measures the profitability of the firm as a whole
in relation to the assets employed. It is frequently referred to as the return on investment
(ROI). The ratio is calculated by dividing earnings by assets. However, there are three
possible definitions of earnings: earnings before interest and tax (EBIT), earnings before
interest but after tax (EBIAT) which is more commonly referred to as net operating profit
after tax (NOPAT), and net profit which is after interest and tax (NPAT). We will apply these
definitions to the Typical Limited financial statements using total assets as the denominator.
282
​
​ = 19.65% (20.1 = 31.67%)
Return on assets (ROA) = __________
​  EBIT  ​ = ___________
1 227 + 208
total assets
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FINANCIAL STATEMENT ANALYSIS
5-23
128 + (100 × 0.72)
_________________
​
​= 13.94% (20.1 = 22.32%)
​  NOPAT  ​ =
Return on assets (ROA) = __________
1 227 + 208
total assets
128
NPAT  ​ = ___________
​
Return on assets (ROA) = ​ __________
​ = 8.92% (20.1 = 17.95%)
1 227 + 208
total assets
In the case of Typical Limited, irrespective of how earnings are defined, the return on total
assets has declined from 20.1. It could be said from the above analysis that, irrespective of
how earnings are defined, the assessment will be the same. This will not always be the case.
Deciding which definition of earnings should be used depends upon the objectives of the
analysis.
■■ Using earnings before interest and tax is useful for comparing firms in different tax
situations and with different degrees of financial leverage.
■■ Using earnings before interest but after tax (NOPAT) is conceptually the most correct
approach. The reason for this is that it excludes interest, which is a cost of financing, but
includes taxation that is an operating cost.
■■ The final interpretation of earnings is to use net profit after interest and tax. This tends to
understate the return as the after-tax cost of debt finance has not been removed. In this
case the degree of financial leverage will have an impact on the return on total assets.
The returns on assets were based on total assets. However, it may be more useful and relevant
to determine the return on net operating assets, which are total assets less current liabilities
(excluding short-term debt). This is also termed return on capital employed (ROCE), due to
capital employed being defined as the long-term capital raised to finance operations, that is,
long-term debt plus equity or total assets less current liabilities. However, short-term debt
should normally be excluded from current liabilities. Also, it would be correct to exclude
non-operating financial investments and excess cash from total assets. Remember that it is
important to be consistent so we should divide operating income by net operating assets.
Furthermore, within the context of analysing value creation, the conceptually correct
definition of return on capital employed is net operating profit after tax (NOPAT) divided by
net operating assets. Instead of the term return on capital employed (ROCE), other terms
often used are return on invested capital (ROIC), as well as return on net assets (RONA),
which we will treat as equivalent. If we apply this to Typical Limited, we get the following:
128 + (100 × 0.72)
NOPAT
_________________
​
Return on Capital Employed (ROCE) = ​ __________________
​ = ​
Net operating assets
1 435 − 98
= 14.96% (20.1 = 23.91%)
Note that the current liabilities deducted above must relate to operating activities. For
example, the current portion of long-term loans and other interest-bearing debt included
in current liabilities is not deducted from total assets to derive net operating assets when
calculating ROIC or ROCE.
A straightforward definition of invested capital or net operating assets is working capital
plus fixed assets. In the case of Typical Limited, the current liabilities of R98m is assumed
to relate to operations as this relates to trade and other payables. It is best to exclude shortterm interest-bearing borrowings from operating current liabilities.
128 + (100 × 0.72)
NOPAT
Return on Invested Capital (ROIC) = ​ ______________
​ = _________________
​
​= 14.96%
Invested capital 1 227 + (208 − 98)
In line with Economic Value Added (EVA) covered later in the chapter, if ROCE or ROIC
is calculated, as defined above, then it can be compared to the firm’s weighted-average cost
of capital (covered in Chapter 7), in order to determine whether value has been created or
destroyed. A firm’s weighted-average cost of capital (WACC) is the average cost that it pays
on its long-term sources of finance. Therefore, if ROCE or ROIC exceeds WACC, the firm
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FINANCIAL MANAGEMENT
has generated more from its investment in net operating assets than it needs to pay to its
providers of debt and equity finance and so value has been created. Conversely, if WACC
exceeds ROCE or ROIC, then the firm has destroyed value.
If we calculate ROIC based on average invested capital (average fixed assets plus average
current assets less average non-interest bearing liabilities), then ROIC would be:
128 + (100 × 0.72)
_________________
NOPAT
​ = ​
​
Return on Invested Capital (ROIC)= ______________________
​
Average invested capital 1 182 + (196 − 93)
= 15.57%
In this case, it is immaterial whether we use the average or the closing values of invested
capital. However, it is important to use average invested capital if there has been a material
change in the invested capital from the prior year. We have assumed that the cash is operating
cash, but if this is excess cash, then we need to deduct this from invested capital as we are
comparing operating income relative to operating assets.
Bidvest reported a pre-tax ROIC of 18% for 2018. Although Bidvest earned an operating margin
on sales of 8.4%, its return on invested capital is much higher. As the cost of capital of Bidvest
is likely to be around 11%, Bidvest has created value. Shoprite’s ROIC (if we exclude its R7.5
billion cash and cash equivalents from its net operating assets) is high at 23%.
Barloworld in its 2017 Integrated Report indicated that its ROIC of 10.3% was lower than its
weighted average cost of capital of 12.3% but it also broke down its ROIC per division as follows:
Barloworld is focused on turning around the Logistics division and exiting certain areas of
operation.
In the USA, McKinsey reported for over 5000 non-financial companies that the median
ROIC over the period 1963–2008 was about 10%, although the median ROIC has increased
in more recent years. Sectors such as pharmaceuticals and personal products that are based on
patents and brands reported ROICs of 15–20% while sectors such as utilities, airlines and paper
reported ROICs of only 5–10%. High ROIC companies tend to experience a fall in ROIC within
10 years but high ROIC companies tend to sustain their advantage over low ROIC companies
over time. However, a high ROIC may be due to writing off R&D and advertising costs.
Return on equity. The ratio of net profit after interest and taxes to ordinary equity measures
the return on equity. If we apply this to Typical Limited we get the following:
net profit
128 ​= 13.99% (20.1 = 28.21%)
​ = ​ ____
Return on equity = _____________________
​
total shareholders funds 915
From this ratio it can be seen that the return on shareholders funds has declined significantly
over the two years. This is to be expected, given the increased costs and decline in the other
profitability ratios.
Bidvest earned a return on equity of 15.6% in 2018. Shoprite earned a return on equity of
19%. In contrast, Kumba Iron Ore earned a return on equity of 75% in 2013 but this declined
in line with the fall in the iron ore price. The Kumba ROE in 2017 was 35.4%.
Cash flow ratios
Cash flow is the essence of any business. If the cash flow is inadequate, the firm will be
unable to meet its future financial obligations and will be forced ultimately to either curtail
or cease operations. As a result, most analysts consider the analysis of cash flow as one of
the best indicators of financial stability. Further, research studies have found that the cash
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flow to total debt ratio is a reliable indicator of financial distress.
Cash flow to total debt. This cash flow ratio measures the cash flow generated from trading
activities in relation to total debt. The ratio is calculated as follows:
cash flow from operations ____
_______________________
​ = ​  239 ​= 56.63%
​
Cash flow to total debt =
422
total debt
This ratio reflects the ability of Typical Limited to generate cash flow and it is clear from
this ratio that the company is unlikely to suffer from financial distress. No comparative is
available as only the 20.2 Statement of Cash Flows is given.
We have included long-term and short-term debt in the denominator. To be more
prudent, we could have used operating cash flow after capital expenditure, which would
result in a cash flow to debt ratio of only 6.87% [(239 − 210)/(400 + 22)].
Market value ratios
These ratios indicate the relationship of the firm’s share price to dividends and earnings.
They are indicators of what investors think of the firm’s past performance and future
prospects. If the firm’s liquidity, asset management, debt management, and profitability
ratios are all good, investors will value the shares of the firm highly and the market value
ratios will be high.
Dividend yield ratio. The dividend yield ratio indicates the return that investors are obtaining
on their investment in the form of dividends. The share price for Typical Limited was R2.80
at 30 June 20.2 (R3.75 in 20.1). The ratio is calculated as follows:
dividend per share _____
Dividend yield = ​ ________________
​ = ​  10.6c ​= 3.79% (20.1 = 5.28%)
280c
price per share
The dividend yield is higher than the average dividend yield on the JSE. The current total
dividend yield for the JSE is between 2–3%. See Chapter 16 for more on dividend yields
in South Africa. In the long term, shareholders would earn both dividends and capital
appreciation, and so the total return would be considerably higher than the dividend yield.
Earnings yield. The earnings yield is calculated by taking the earnings per share and dividing
it by the market price of the share. This ratio indicates the yield that investors are demanding.
Applying the ratio to Typical Limited we get the following:
earnings per share _____
​ = ​  25.6c ​= 9.14% (20.1 = 12.64%)
Earnings yield = ​ ________________
280c
price per share
Price–earnings ratio (P/E). A similar ratio to the above is called the price–earnings ratio. The
price–earnings ratio also shows how much investors are willing to pay per rand of reported
profits. This ratio is, in fact, the inverse of the earnings yield, being the price per share
divided by the earnings per share. Thus the price is regarded as being a multiple of the year’s
earnings. Applying this to Typical Limited we arrive at the following:
price per share
280c  ​= 10.94 times (20.1 = 7.91 times)
________________
_____
Price–earnings ratio = ​
​ = ​
earnings per share 25.6c
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Generally, price–earnings ratios are higher for firms with high growth prospects and lower
for firms that are regarded as being risky. The marked increase in the price–earnings ratio is
probably the result of the drop in earnings. The average price–earnings ratio in South Africa
in 2018 was about 17.
The price–earnings ratio of Tiger Brands was 13. In contrast, Clicks was on a P/E ratio
above 30 in 2018, indicating market expectations of a high growth in earnings in the future.
Dividend cover. Another ratio which is not based on market values yet affects market values is the
dividend cover ratio. This ratio measures the extent of earnings that are being paid out in the form
of dividends. A high dividend cover would indicate that a large percentage of earnings is being
retained and reinvested within the firm, while a low dividend cover would indicate the converse.
earnings per share 25.6c
​= 2.42 times
Dividend cover = ​ ________________
​ = ​ _____
dividend per share 10.6c
[20.1 = 2.39 times]
This ratio indicates that the dividend cover has increased marginally and that Typical
Limited is paying out some 40% of its earnings as dividends, while the balance is reinvested
on behalf of the shareholders.
6 STRUCTURED RATIO ANALYSIS
So far we have examined a number of important ratios and analysed them by comparing
them to both ratios from previous years and industry averages. We can combine these ratios
to obtain an overall picture of the company. This is often referred to as structured analysis.
Du Pont analysis
The Du Pont model is a frequently used structured analysis technique. Figure 5.2 displays a
modified Du Pont analysis for X Limited, and includes industry comparisons where applicable.
As the objective of financial management is the maximisation of wealth, a structured
analysis should aim towards measuring how effectively this objective is achieved. The
Du Pont model uses the return on equity as the overall indicator of success. While profit
maximisation would not be a primary objective, a satisfactory return on shareholders’ funds
would be required to maximise wealth.
The strength of this model lies in its ability to arrange many possibly confusing financial ratios
into three broad categories: those associated with income, those associated with investment
(activity), and those associated with capital structure. These broad categories are reflected in
Figure 5.2. The diagnostic capability of the model allows attention to be focused on the problem
areas rather than haphazardly proceeding through a time-consuming unstructured analysis.
In applying the Du Pont analysis to X Limited, we notice some important characteristics
about the company. The return on equity is significantly better than the return on equity
made by the industry. Moving across in the chart from left to right will help us understand
why this is so. It can be seen that two factors make up the return on equity – firstly, the return
on assets and, secondly, the financial leverage multiplier (FLM). The first is a measure of
income in relation to total assets and the second is a measure of assets financed by ordinary
equity. When these two ratios are multiplied, the result is the return on equity.
This relationship is explained by the following formula:
net profit
total assets
​ × ​ __________
​
ROE = __________
​
equity
total assets
By cancelling total assets we get:
net profit
ROE = _________
​
​
equity
We can further expand this to include the net profit margin on sales.
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net profit ______
sales  ​ × ​ ______
assets  ​
​ × ​ assets
​
ROE = _________
equity
sales
NP%
ROA
ROE
In Figure 5.2, X Limited has achieved a ROE of 35.9% as compared to the industry
sector ROE of 13.4%. Yet when we break this down we find that this was because
the company achieved a higher net profit margin of 5.56% as compared to 4.1% for
the sector and also managed to make a more efficient utilisation of its assets. The
company’s asset turnover of 2.07 compares favourably to the sector’s asset turnover of
1.6. The net result is that X Limited has a return on assets of 11.51% as compared to a
return on assets of 6.56% for the sector. However, the company also makes greater use
of financial leverage resulting in an ROE that is close to 3 times higher than the sector.
The use of financial leverage to bolster ROE may mean that the company is subject
to higher risk than the sector. The Du Pont analysis indicates that it is the combined
impact of focusing on achieving a higher net profit margin on sales, of generating a
greater amount of sales from its assets and making greater use of debt that results in a
much higher ROE than the sector.
X Ltd R58 840
Figures in R000
Net profit
X Ltd 5.56%
Net profit
margin
X Ltd 11.51%
ROA
4
Income
X Ltd R1 058 679
Ind 4.1%
Sales
×
X Ltd R63 247
X Ltd R1 058 679
Ind 6.56%
Sales
Fixed assets
X Ltd 2.07 x
Total asset
turnover
+
4
X Ltd R510 633
X Ltd R407 271
Total assets
Current
assets
Ind 1.6 x
X Ltd 35.9%
ROE
×
Activity
+
X Ltd R40 115
Ind 13.4%
Other assets
X Ltd R510 633
Total assets
X Ltd 3.12 x
Financial
leverage
multiplier
Ind 2.05 x
Capital
structure
4
X Ltd R163 926
Ordinary
equity
Figure 5.2 Du Pont analysis for X Limited
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This is the kind of interrelationship that occurs throughout the chain of indicators in the Du
Pont model. A brief analysis of these interrelationships indicates that X Limited’s high return
on equity is the result of both high financial leverage and a higher-than-average return on
assets. Likewise the return on assets is a combination of an above industry net profit margin
accentuated by a higher asset turnover relative to the industry ratio. While this type of analysis
has many benefits, the major one is that it gives us an overall understanding of the firm.
7 FAILURE PREDICTION
Although ratio analysis provides insight into a firm’s operations, the interpretation is
subjective rather than objective. As a result it relies on the perception of the analyst. For
example, a company may have a current ratio that is significantly weaker than that for the
industry. Exactly how bad is this situation? Is this bad enough to cause concern? To what
extent could the interest cover or debt ratio offset the weak current ratio?
As a result of analysts requiring more objective assessments, predictive models based on
ratios have been developed. Most of the research to date has been applied in connection
with the prediction of financial distress and multivariate discriminant analysis (MDA) has
been used to classify companies as subject to financial distress or not. This classification is
made on the basis of each company’s characteristics as measured by its financial ratios.
Financial distress models
The best known of these models was developed by Edward Altman who applied MDA to a
sample of companies and developed a discriminant function that classified companies either
as failed or successful. Altman’s model is as follows:
Z = 1.2 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 + 1.0X5 (Formula 5.1)
Where: X1 = working capital/total assets
X2 = retained earnings/total assets
X3 = earnings before interest and taxes/total assets
X4 = market value of equity/book value of total liabilities
X5 = sales/total assets
Altman found that companies with a Z-score above 2.99 were unlikely to fail and companies
with Z-scores below 1.81 were likely to fail. Altman found that a zone of uncertainty existed
from 1.81 to 2.99. This meant that if the model was applied to a company and a score
of between 1.81 and 2.99 was obtained, a classification could not be made with certainty.
However if the score was below 1.81, the company was almost certain to fail while if the
score was above 2.99, the company was almost certain to succeed.
A similar model was developed in South Africa by Dr J. H. de la Rey at the Bureau of
Financial Analysis in Pretoria. The model is as follows:
k = –0.01662a + 0.0111b + 0.0529c + 0.086d + 0.0174e + 0.01071f – 0.068811
(Formula 5.2)
where: a = total outside financing/total assets × 100%
b = profit before interest and tax/average total assets × 100%
c = total current assets + listed investments/total current liabilities
d = profit after tax/average total assets at book value × 100%
e = cash flow profit after tax/average total assets × 100%
f = total stocks/inflation-adjusted total assets × 100%
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This model achieved a 96% success rate in classifying the companies in the sample as either
financially failed or financially sound. For practical purposes, the model was developed in
such a way that the point of separation between financially sound and financially failed firms
is zero. The further a firm moves above zero, the more financially sound the firm will be. On
the other hand if the result becomes negative, the firm is likely to fail financially. A zone of
uncertainty exists from –0.2 to +0.2, which means that a result in this area is inconclusive.
Altman has updated and improved his original model with the new Zeta model. Little
information is available about this model as it is used as a basis for a credit rating financial
service that is offered by Zeta services. It is claimed that the newer model can predict
financial distress with a greater degree of accuracy than the previous model.
Further, in the mid-1990s Altman modified the Z-score and devised the Z (EM) model
to evaluate non-manufacturers and companies in emerging markets. The sales/total assets
ratio was excluded and the market value of equity is replaced by the book value of equity.
This model has successfully been applied in South Africa and in other emerging economies.
The Z model is set out as follows:
Z = 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4
(Formula 5.3)
Where: X1 = working capital/total assets = (current assets – current liabilities)/TA
X2 = retained earnings/total assets
X3 = EBIT/total assets
X4 = book value of equity/total liabilities
The Z score critical barriers are set as follows:
Z > 2.60 “Safe” Zone
1.10 < Z < 2.60
“Grey” or “Danger” Zone
Z < 1.10
“Distress” or “Fail” Zone
According to research by William Beaver, the cash flow to total debt ratio was found to be the
most useful single ratio to predict corporate failure. There are other proprietary methods
in use such as the H-Score® by Company Watch and Moody’s KMV methodology which is
based on a proprietary option pricing model and other risk metrics to predict failure.
8 LIMITATIONS OF RATIO ANALYSIS
While ratio analysis is very useful for evaluating performance, there are limitations that
need to be considered before it is applied mechanically:
■■ Some firms are diversified into different industries and it is therefore misleading to
compare such firms against one set of industry averages. In order to provide additional
information, companies provide segmented reporting which outlines the contribution
made by each line of business to sales, total assets, operating income, and return on
assets.
■■ In many instances management would strive to be up with the sector leaders, in which
case it might be preferable to make comparisons with firms that are regarded as being
sector leaders.
■■ In making inter-firm comparisons, or comparing against industry averages, the effect of
different accounting policies must be considered. As International Financial Reporting
Standards are issued, these problems are reduced but not entirely eliminated.
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■■
■■
■■
■■
■■
FINANCIAL MANAGEMENT
In making a comparative analysis, the timing of year-ends should be considered for both
of the firms being compared or the industry average. This timing could lead to ratios
being affected by seasonality. The inventory turnover ratio, for example, would be fairly
sensitive.
It is possible for a firm to “window dress” its financial statements, thus reflecting an
improved financial position. For example, Worldcom capitalised operating expenditure
while Leisurenet used a revenue recognition policy that recorded revenue up front. In
this way both companies managed to show substantially increased profits although their
cash flow continued to deteriorate. Leisurenet’s main operating assets, its gyms, were
acquired and later sold by Richard Branson (Virgin Active).
It is difficult to assess how bad or how good a ratio is. This subjective assessment will
depend upon the perception of the analyst. Furthermore, some ratios might indicate
strong points while others might indicate weak points and it is difficult to assess to what
extent the strong points offset the weak points. However, as mentioned in Section 7 on
failure prediction, effective models can be established to avoid such a problem.
As financial statements are normally prepared on a historic cost basis, unadjusted
for inflation, the accounting amounts are removed from economic value. This will be
reflected by the understatement of fixed assets and possibly inventory, while the value of
long-term debt will decline in real terms. This results in equity being understated. These
factors make ratio comparisons over time for a given firm, and across firms at a given
point in time, less reliable than would be the case in the absence of inflation.
Also, a company may have a high ROA only because the company owns very old and
depreciated plant and equipment. This makes it difficult to compare this company’s
ROA to another company that has newer assets on the Statement of Financial Position,
which would have been purchased at a higher cost. The newer assets also have higher
book values as they have a longer time to be depreciated.
Where companies do use fair value and mark-to-market accounting to value assets and
liabilities in financial statements, we need to evaluate the assumptions used to value the
assets or liabilities. For example, are the assumptions used to value employee share options
reasonable? Is the discount rate used valid?
The above limitations do not negate the usefulness of ratio analysis but it is important
that analysts should be aware of them and make the necessary adjustments. Applying ratio
analysis blindly, using a procedural approach, is dangerous as the effectiveness of the exercise
depends upon the interpretation of the ratios by ­­– and hence the skill of – the analyst. If
an analyst applies ratio analysis perceptively, ratios will provide useful insights into a firm’s
operations. This skill is acquired through experience and from a thorough understanding of
financial statements and a company’s business.
9 ECONOMIC VALUE ADDED (EVA)3
Economic Value Added (EVA) is a financial performance measure that tries to capture the
true economic profit of an enterprise. EVA is also a performance measure which is linked to
the creation of shareholder wealth over time. It is claimed that by implementing a complete
EVA-based financial management and incentive compensation system, managers will obtain
superior information – and superior motivation – to make decisions that will create the
greatest shareholder wealth in any publicly owned or private enterprise.
Put more simply, EVA is net operating profit minus an appropriate charge for the
opportunity cost of all capital invested in an enterprise. As such, EVA is an estimate of true
3
EVATM is a registered trademark of Stern Stewart & Co.
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“economic” profit, or the amount by which earnings exceed or fall short of the required
minimum rate of return that shareholders and lenders could get by investing in other
securities of comparable risk.
EVA = Net Operating Profit after Tax (NOPAT) – {Capital × The Cost of Capital}
The capital charge is the most distinctive and important aspect of EVA. With traditional
financial analysis, many companies may appear profitable while in fact they are not. When
a business returns a profit that is less than its cost of capital, it does not create wealth; it
destroys it. EVA corrects this error by explicitly recognising that when managers employ
capital they must pay for it, just like any other expense.
By taking all the capital costs into account, including the cost of equity, EVA shows the
rand amount of wealth a business has created or destroyed in each reporting period. In
other words, EVA is profit the way shareholders define it. If the shareholders expect, say,
a 20% return on their investment, their wealth will only grow to the extent that their share
of after-tax operating profits exceeds 20% of equity capital. Everything before that is just
building up to the minimum acceptable compensation for investing in a risky enterprise.
For example, assuming that the cost of capital for Typical Limited is 16%, the EVA
would be calculated as follows:
Despite having generated a profit of R128 million in 20.2, the return is below the cost of
capital and so shareholder value has been destroyed by an amount of R14 million.
EVA was developed to help managers incorporate two basic principles of finance into
their decision-making. The first is that the primary financial objective of any company
should be to maximise the wealth of its shareholders. The second is that the value of a
company depends on the extent to which investors expect future profits to exceed or fall
short of the cost of capital. By definition, a sustained increase in EVA will bring an increase
in the market value of a company. This approach has proved effective in virtually all types
of organisations; from emerging growth companies to turnarounds. This is because the
current level of EVA is not what really matters. Current performance is already reflected in
share prices. It is the continuous improvement in EVA that brings continuous increases in
shareholder wealth.
EVA has the advantage of being conceptually simple and easy to explain to non-financial
managers. It starts with familiar operating profits and simply deducts a charge for the capital
invested in the particular business unit. By assessing a charge for using capital, EVA makes
managers care about managing assets as well as income, and helps them properly assess
the trade-offs between the two. This broader, more complete view of the economics of a
business can make dramatic differences.
Most companies use a number of measures to express financial goals and objectives.
Strategic plans often are based on growth in revenues or market share. Companies may
evaluate individual products or lines of business on the basis of gross margins or cash flow.
Business units may be evaluated in terms of return on assets or against a budgeted profit
level. Finance departments usually analyse capital investments in terms of net present
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value, but weigh prospective acquisitions against the likely contribution to earnings growth.
Bonuses for line managers and business-unit heads typically are negotiated annually and
are based on a profit plan. The result of the inconsistent standards, goals, and terminology
usually is a lack of cohesive planning, operating strategy, and decision-making.
EVA being a single financial measure links decision-making with a common focus –
how to improve EVA? EVA provides a common language for all employees and allows
management decisions to be modelled, monitored, communicated and compensated in a
single and consistent way – always in terms of the value added to shareholder investment.
A related indicator is a firm’s Market Value Added (MVA). This is the difference between
the book value of the firm’s equity and its market value.
Sometimes firms’ EVA and MVA figures do not reconcile, either because the market
expects a fall in future EVAs or the market may have had a temporary adjustment in value.
The use of EVA to measure performance
Whilst our view is that EVA or Economic profit is relevant, very few listed companies on the
JSE have disclosed the use of EVA or Economic Profit in their integrated report or annual
financial statements4. Distell in 2018 did disclose that they apply Economic Profit to evaluate
performance and reported the following:
Distell was able to generate a positive economic profit of R325.7m in 2018, which was 17%
higher than the previous year. SABMiller, a South African based global brewer with operations
in over 40 countries, was acquired by AB InBev in 2017. SABMiller disclosed its EVA in its
annual report for 2005. Sales in 2005 were $14.53bn. The group stated the following at the
time:
As noted previously, SABMiller is continually investing in new brewing operations and most new
investments impact negatively on EVA in the short term. Key factors to be borne in mind are:
EVA is calculated using operating profit after tax, adjusted for exceptional and non-recurring
items; the capital charge is calculated on opening economic capital – adjusted for acquisitions,
any impairments of assets of continuing business units, and goodwill previously eliminated against
reserves.
After 2005, SABMiller no longer disclosed its EVA and we estimated that the group would
have recorded years of negative EVAs before becoming EVA positive again from about 2012.
We have retained this example from 2005 as it is instructive of how a major South African
based (but listed in London) group determined its EVA. This is reflected in Table 5.8.
There are a number of listed companies that will disclose their weighted average cost of capital (WACC) and
we have referred to Barloworld in this chapter and other companies in Chapter 7 on the Cost of Capital. A few
companies will refer to their ROIC in relation to their WACC in order to indicate how they are creating value.
4
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Table 5.8 Determination of EVA by SABMiller (now a division of AB InBev)
Perspectives on EVATM by Joel Stern
Professor Joel Stern has been at the forefront of advancing the cause
of shareholder value management and is the founder of Economic
Value Added (EVA). He is CEO of Stern Stewart. Joel has written
or co-authored eight books, and writes for the Financial Times and
the Wall Street Journal. He is associated with a number of graduate
schools and has taught at Columbia and UCT for many years.
EVA is often described as trading profit minus a capital charge for debt and equity capital.
Perhaps more clearly, it is total capital multiplied by the spread, the rate of return on total
capital (ROTC) minus the weighted average cost of capital (C):
EVA = TC [ROTC – C]
This encourages management to maximise performance by:
• Growing the firm (increase TC) but only if ROTC exceeds C;
• Improving performance on existing capital (↑ ROTC); and
• Harvesting losers and disgorging cash to shareholders (↓ TC and ROTC – C becomes
larger on the remainder).
My message, however, is more complex than just measurement. To achieve value-enhancing
behaviour, management needs to reinforce the asset management process by prioritising
the process in terms of declining order of EVA improvement, accompanied by an incentive
compensation system tied to sustainable EVA improvement, where a portion of incentive
declarations are paid out now, the rest held at risk subject to loss if sustainable results fail to
be achieved.
Although discounting expected future free cash flows yields firm value, it is possible, even
desirable, for free cash flow (FCF) to be negative when firms have projects with expected returns
above the cost of capital. The practical problem is that incentive contracts cannot be written on
FCF, since negative FCF can be beneficial. EVA improvement always means value improvement,
so incentives based on EVA are congruent with shareholder needs.
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10 WHAT’S BEHIND THE NUMBERS?
Ratio analysis is based on accounting numbers and their value is dependent on the quality
and the integrity of the accounting data that make up the financial statements. The
company’s financial statements will be subject to an independent audit and the company
should adhere to generally accepted accounting principles and the International Financial
Reporting Standards (IFRS). Whilst there are instances where this may not apply, the fact
remains that management has sufficient flexibility to significantly impact on the results of
the company and yet remain safely within the rules. The company may do so by selecting
accounting policies that enable the company to present results that favour its point of view
and still remain within the boundaries of IFRS.
There are other distorting effects such as comparing companies, when one has newer
plant and equipment and reports significantly lower returns on assets and the other may
have older and fully depreciated assets resulting in high returns. The effect of using historical
cost in the Statement of Financial Position results in objective and verifiable costs at the
expense of more subjective but relevant data. Management may also be driven to make
accounting choices which do not adhere to accounting rules.
There are a number of important factors to understand when we evaluate the quality of
accounting data and disclosure.
Understand the business and the industry sector
It is important to understand the business. Warren Buffett understands Gillette (Procter
& Gamble) because millions of people get up and shave in the morning, but he does not
understand the economics of the Internet and avoided the boom and the bust of the IT
companies. In the past, the automobile sector revolutionised transport but of the few
thousand motor manufacturers in the USA, there are only three that remain. Investing in
this sector initially may have cost you money, although it would have been a good idea, as
Buffett states, to go short on horses.
What are the company’s strategies? Undertake a strategic analysis of the industry and
the company by evaluating the company’s products, the position of the buyers and suppliers
and the competitive landscape. Are the products subject to foreign competition and at risk
of technological obsolescence? Does the company own strong brands? Does the company
own patents? Do the accounting policies adopted by the company make sense in terms of
the company’s business model? Does the company adhere to the norms of the industry
sector?
Understand management’s motives for selecting accounting policies
We need to relate the accounting policies adopted by the company to any inherent motive
that management may have to state returns and assets in a certain way. What are some of
the issues facing management that may influence the choice of accounting policies?
Loan covenants. The banks may impose limits on a number of accounting ratios such
as interest cover and working capital ratios. This means that if a company is in danger of
violating its loan covenants, it is more likely to select accounting policies that will reduce the
likelihood of the company transgressing its loan covenants.
Management incentives. If management’s remuneration is tied to the company’s accounting
results or even the company’s share price, in terms of share options or bonuses, then
management may select accounting rules that will maximise company profitability to ensure
increased remuneration levels.
Taxation. A company may select policies that will result in the company incurring a lower
tax liability.
Regulatory issues. If a company operates in a regulatory environment, then it may select
accounting policies that will optimise its position in relation to the regulatory authority. For
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example, a utility’s cost of capital will be used by a regulatory authority to determine the
pricing of the company’s products and services. The utility will use parameters that increase
its cost of capital and use accounting policies that will increase the value of its assets and
reduce its level of accounting profitability. The company may select accounting policies to
reflect low returns if the industry is subject to regulatory review.
There are a number of other issues. For example, if a company is subject to a takeover,
the company will wish to quickly increase its earnings to push up the price and thereby make
the offer much more unattractive.
Understand the key drivers of value
Each industry sector will have a few key ratios that are critical to that industry. For example,
the operating margin for the retail sector is important. If Shoprite is able to increase its
operating margin from 2.0% to 6%, then this is critical for the valuation of the company.
Inventory control is critical in the retail sector and working capital ratios are very important
in evaluating company performance. In the banking sector, the evaluation of credit risk and
managing interest rate spreads is critical. For manufacturers, the productivity of capital
and capacity utilisation is important and there is a focus on asset turnover and returns on
invested capital. In the pharmaceutical sector, the level of R&D to sales is relevant and for
companies with highly branded products, the management of brands and the investment in
advertising are important.
Understand which accounting policies are flexible
It is important to evaluate which accounting policies offer flexibility. Which depreciation
policy does the company use and what are the expected useful lives of the company’s
assets? Are the company’s operating leases really operating leases or finance leases that
have circumnavigated the rules? What is the company’s policy in relation to research
and development costs? What is the company’s revenue recognition policy? What is the
company’s allowance for bad debts and inventory obsolescence? Does the company’s
provision for warranty claims reflect economic reality?
Accounting for leases
In terms of IFRS 16, all leases are required to be capitalised from 2019. This means that
companies are required to disclose right-of-use asset values in the Statement of Financial Position
in relation to leases as well as the present values of lease payments as liabilities. This alters,
sometimes fundamentally, some of the financial ratios of companies before and after IFRS16
came into force in 2019. A leased asset is treated as an owned asset and is depreciated over its
useful life or the term of the lease. In this case, lease payments are separated into two components
– interest and the repayment of principal. This is similar to the buy and borrow option.
In contrast, up to 2019, operating lease obligations did not appear in the Statement of
Financial Position (balance sheet) and lease payments were treated as an operating expense.
Operating leases represented a significant source of “off-balance sheet” financing up until
2019. The following are some of the effects of the change in lease accounting in 2019 will have
as compared to prior years:
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■■
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Increase in assets and liabilities for most companies, particularly companies operating in
sectors such as airlines, retailing and logistics
Lower asset turnover ratios
Increase in debt/equity and debt ratios
Increase in current liabilities and decrease in the current ratio
For new leases, there will be an initial decrease in net income, as interest plus depreciation
in the early years will exceed the operating lease payment. In later years, this will reverse and
net income will increase as interest falls with the fall in the principal amount owing
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Increase in operating income and operating cash flow as this will no longer include operating
lease payments
Increase in EBITDA
Lower ROIC.
The requirement to capitalise all operating and finance leases reflects what Stern Stewart,
credit rating agencies and analysts have been doing for many years to calculate EVA, analyse
financial statements and evaluate credit risk5. However, we need to be aware that companies
may switch to “outsourcing” contracts, or service contracts or franchising arrangements and
may restructure the ownership of operations so that capital and liabilities are excluded from
group accounts. For example, Coca-Cola either does not own or only owns a minority stake
in many of the bottling plants. This means that the company does not have to consolidate the
capital-intensive bottling plants on its own Statement of Financial Position which will have
a negative impact on its ratios. Coca-Cola has long-term “franchising” contracts with the
bottling plants. A lease contract may include service or maintenance components which need
to be separated from the lease component and be included as operating expenses.
Understand the warning signs
What are some of the warning signs pointing to problems with the company’s financial
report? What are the so-called “red flags” relating to accounting disclosure and practice?
The following may reflect potential problems in relation to business and accounting practices:
■■ Increase in accounts receivable that exceeds the increase in sales. This may reflect the
company pushing sales into its distribution channels which may be returned, or it may
reflect a relaxation of credit policy which may result in an increase in bad debts in the
following year.
■■ Increase in inventory that exceeds the increase in sales. This may reflect faltering demand
for the company’s products or a fall in economic activity that will result in lower demand
in the next year. This may lead to write-downs or lower margins on sales. However, an
increase in inventory may also reflect an expectation of increased sales in the next year.
Where is the increase occurring? Is it in materials, work-in-process, or finished goods?
Does it reflect increased returns from the distributors? Watch any increase in workin-process as this may reflect operational problems and some companies may use this
account to hide assets and projects that have no value.
■■ Restructuring, non-recurring charges and asset write-downs or sales. The misuse of
restructuring charges to create reserves and bolster future returns is well recognised
and investors should evaluate the validity of each charge. What are reasons for the
charge? Also if a company often reports non-recurring charges or significant writedowns, then it may mean that the company is not able to react in time to a changing
business environment. The industry sector itself may be at risk. Sometimes to hide poor
operating results, a company may engage in asset sales, realising a large profit on asset
sales to bolster revenue and earnings per share.
■■ Accounting income and tax losses. Watch out for companies that consistently report
positive accounting income and yet continue to incur tax losses. Whilst this is quite
possible, at least for a short period, it is not sustainable and may reflect dubious
accounting practices. There may be good reasons for a company reporting different
incomes for financial reporting and tax purposes, yet we would expect there to be a
consistent relationship between the company’s reported accounting income and its
taxable income. A changing relationship between accounting income and taxable
income is a warning sign.
A rule of thumb was to multiply the annual rental or lease charge by 8 in order to estimate the present value
of lease payments.
5
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Accounting income and a negative operating cash flow. Focus on the company’s cash
flow statement. A company that is reporting accounting income and yet is consistently
reporting a negative cash flow is heading for the rocks. Whilst this may happen for
good reasons, such as significant capital investments which will bolster future sales and
operating returns, it may also reflect a company chasing growth at all costs even when
returns are lower than the company’s cost of capital. It is important to evaluate the
company’s accounting policies and analyse the differences between the Statement of
Comprehensive Income and the Statement of Cash Flows. Evaluate the investments in
relation to the potential of the company, the sector and the size of the company and its
stage of expansion and development.
Complex company structures and related party transactions. Companies may use complex
structures and related party transactions to hide problems. Enron used special purpose
entities to take liabilities off its Statement of Financial Position and yet retained the
credit risk of such transactions. Do you understand the company structure? Does it
make sense in terms of the company’s business model and operations?
Accounting policies in relation to research and development, depreciation and leasing.
Companies may decide to capitalise R&D costs in order to bolster earnings and
may select long asset useful lives to reduce the annual depreciation charge. Further,
companies may lease assets over a number of years and avoid the classification of such
leases as finance leases by estimating long useful lives for the underlying assets. For
example, a plane may have an estimated useful life of 25 years and so a lease for 15
years will not fall within the rules requiring that the lease be classified as a finance lease.
This will understate the asset base and overstate the company’s return on assets.
Accounting practices that are at variance with the norm for the industry sector. If a company
adopts accounting policies that are at variance with other companies in the sector, then
this may reflect problems with the quality of the accounting data. Evaluate the reasons
why the company has adopted different policies.
Lack of corporate governance. A lack of good corporate governance policies may
mean that the CEO may exercise too much power and the accounting practices
may be overly influenced by the CEO’s view. Independent directors and audit
committees act as a counter-balance and ensure a greater credibility in relation to
the accounting numbers.
Changes in auditors, qualified opinions or published disagreements with the auditor. A
published disagreement with the auditor over the choice of an accounting policy
or a change in auditors for no apparent reason may indicate future problems. A
qualified audit report is certainly a problem. Auditors are increasingly subject to
litigation risk and will be likely to disagree with company policies which do not fall
within the ambit of generally accepted accounting practice. Also, we need to be
careful when a large company appoints a small auditing firm whereby fees from the
company becomes a dominant source of income for the auditing firm. Research
indicates that large companies audited by small firms are less likely to receive
qualified audit reports.
Changes in revenue recognition policies. It is important to evaluate any change in the
company’s revenue recognition policies. This is a difficult area as it is subject to
interpretation. If a company’s revenue consists of the provision of goods and services over a
number of years, then the difficulties of revenue recognition is compounded. What revenue
should be recognised this year as compared to the next few years? How does the company
attach relative values to the services and the initial product components?
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Vendor financing and financing structures. What if the company making the sale is also
offering finance to the customer. Is this really a sale or more like a loan? Vendor
financing provided impetus to the growth of such companies such as Cisco, but if
economic circumstances change, then the company will not be able to collect its debts
and its products will have little value.
Changes to provisions and reserves. Evaluate any transfers to or from reserves. For
example, banks maintain provisions for bad loans whereby the bank will estimate the
proportion of bad loans it will incur. Yet in a particular year which just happens to be a
year of poor operating results, the bank may reduce the provision for “good” reasons,
but which also happen to save the day in terms of the bank’s level of profitability.
Understand the business and financial risks facing the company
We have identified a number of business risks that companies face in Chapter 10 which are
relevant here. How much is the company dependent on one product, one customer, one
supplier and one geographic market? What is the risk of technological obsolescence? What
is the risk of litigation? Is the company subject to high debt levels? Is the company subject
to substantial competition and what is the growth rate of the industry sector?
Although ratio analysis is important, it is critical to go behind the numbers to evaluate
the quality of the accounting data, the quality of disclosure and to analyse management’s
incentives to use spotlights rather than floodlights on the numbers reported in the company’s
financial statements.
Sensitivity analysis
In Chapter 10 we will explain the use of sensitivity analysis in project evaluation. In financial
analysis, we may also wish to understand how sensitive a company’s operating returns and
ratios are to changes to the key business drivers, such as the selling price, costs and volumes.
For example, Rainbow reported a possible significant decline in its return on assets due to
an increase in the cost of inputs such as feedstock. In explaining its sensitivity to commodity
prices in 2017, Tiger Brands reported that a 10% increase in the price of wheat, maize, rice
and sorghum would reduce profit after tax by R360.1m. This information is useful to analyse
a company as we understand how sensitive operating income and returns will be to changes
in the key business drivers.
Further factors to consider when analysing a company
Other factors may be as important as financial analysis and financial ratios. We have set out
some other factors that may be important in analysing a company. This is not exhaustive but
provides a few indicators of what we should look out for when analysing a company.
Are the directors selling shares in the company?
Whilst we can understand that directors may sell shares for personal reasons to buy a home
or settle family obligations, major sales of shares by directors should be a warning sign.
Alternatively, the purchase of shares indicates that the directors consider the value of the
company to be understated by the market.
Is the company aggressive in recognising revenue in relation to long-term contracts?
It may be prudent to carefully analyse companies that recognise revenue from the entering
into long-term service contracts in the first year, rather than spreading out the revenue over
the term of the contract. It is often difficult to maintain such growth and this often creates
the temptation for the executives to manage earnings to create the impression that growth
is sustainable.
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Is the company aggressive about acquisitions?
Companies that engage in acquiring other companies at a frenetic pace often will make one
acquisition too many that will often lead the company into financial trouble. It is difficult to
integrate and consolidate businesses if the company makes too many acquisitions. This is
made worse if the acquisitions are financed with debt financing.
Are the company’s customers performing well?
If the company’s customers are in financial trouble, then it is only a matter of time before
the customers reduce purchases or place pressure on pricing thereby impacting on the
company’s margins.
Is the company subject to litigation?
Whilst in the USA, litigation may often be spurious and may in fact indicate that the
company is doing well; we need to monitor major litigation cases in process against the
company. Litigation may have significant economic impacts on the company. For example,
miners in South Africa instituted class action lawsuits against mining companies as a result
of suffering from silicosis and lung disease arising from gold mining operations. On the basis
of the numbers of miners subjected to lung disease over time (20−30% of miners contracted
silicosis), this could prove significant to the market capitalisation of a company such as
AngloGold Ashanti, although it pales in comparison to the human cost of this tragic legacy
on miners and their families. In May 2018, the major gold producers reached a R5bn silicosis
settlement with law firms representing thousands of miners. However, there could be further
claims in the future and the amount of R5bn could increase.
Is the company subject to significant operational risks?
Gold mining in South Africa is subject to significant operational risks due to unstable ore
strata and the tremendous depths at which companies are required to mine. In sectors
that companies will experience significant operating risks, we need to carefully monitor
company performance and their approach to risk management. There is no point in actions
that result in cost savings but also result in dramatic increases in operating risks. The case
of Toyota installing faulty accelerator pedals which put buyers at risk and BP’s actions in
the Gulf, reflects break-downs in risk management. BP was responsible for lapses in safety
standards that placed employees, facilities and the environment at risk prior to the major
spill in the Gulf. Drilling at tremendous depths raised the operational risk of BP and it
was alleged that this was compounded by a focus on costs rather than on safety. Further,
trust was destroyed resulting in customer boycotts and significant liabilities for BP and
Toyota. As a financial analyst, if you had focused on the extensive number of violations of
regulations by BP, you would have avoided investing in BP thereby saving money even if
the financial results and ratios were indicating an excellent performance. This was because
the risk had risen.
All companies will have operational risks but it is important to analyse how a company
is managing these risks. Do not just believe what the company says – look at the way the
company acts. You have to often expand beyond the financial statements by analysing
regulatory information and you often need to read between the lines. For example, Rainbow
has set out the major operational risks it faces; being, disease outbreaks at farms, a significant
increase in feed raw material costs, dust explosions and fire. Rainbow has taken measures
to mitigate these risks.
Does the company have insurance to cover major operating risks?
It is important that companies are adequately covered for major risks such as fire, flooding,
accidents and other disasters. Check on the company’s information on insurance.
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Does the company have actual or potential environmental liabilities?
Companies may have extensive environmental liabilities. The South African mining sector
has legacy challenges in relation to mining practices in the past which have resulted in
pollution, toxic underground water and safety hazards due to radioactive sites from uranium
contamination. In some lakes adjacent to mines the water is at the same acidity level as
battery acid. Environmental restoration and rehabilitation is costly and provision needs
to be made for these costs. For example, Harmony, which is one of South Africa’s major
gold producers, is facing significant environmental challenges. Government now requires
companies to make provisions for environmental rehabilitation. Once mining activity
has ceased, the environmental degradation continues. This is particularly relevant in the
Witwatersrand Basin. Environmental liabilities will eventually become a major issue in the
mining sector.
Are there reports of problems with product quality?
As companies engage increasingly in the outsourcing of production and focus more
on cost reduction, there may be impacts on product quality. This has happened to Dell,
Sony (exploding batteries), Toyota (faulty accelerators), food colouring (Sudan I), CadburySchweppes (salmonella), Ford, Firestone, Mittal Toys, and companies in the pharmaceutical
industry. Tiger Brands had a listeria outbreak in a meat processing facility which led to the
tragic death of over 193 people. Product recalls are expensive; not only in terms of cost but
also in terms of damaging a company’s brand name. They can have a significant impact on a
company’s future profitability and sales. There could also be significant litigation arising from
incidents relating to product quality. The market capitalisation of Tiger Brands fell by over
R5.5bn after the listeria outbreak.
Are there reports of any serious issues with its stakeholders such as its customers, suppliers and
employees?
The lack of proper management of labour issues in South Africa’s mining industry has
placed the platinum mining sector at risk and management need to be more proactive
about managing labour relations. Furthermore, safety concerns and fatalities have led
to the closure of mines for periods of time. Companies need to monitor the financial
condition of suppliers as financial distress may impact on the ability of suppliers to
deliver to the company on time without compromising on quality. If its customers are
growing in number, then it is important for the company to increase its capacity in order
to meet the increased demand for its products. If there are reports of product returns from
customers, then this may imply falling standards in product quality that will have financial
consequences.
Does the company have strong brands?
Strong brands create loyal customers and provide a company with protection against
competitors. Yet companies can easily destroy brand loyalty by compromising on product
quality to save costs.
Furthermore, the move by Shoprite, Clicks, Woolworths and Pick n Pay to promote
private labels (house brands) will put pressure on the pricing of branded products.
Does the company communicate well with its shareholders and analysts?
The company should be open in terms of providing information to its shareholders
and analysts. You should look for evidence of how a company communicates with its
shareholders. For example, the CEO of Enron swore at an analyst for asking a valid and
relevant question. This indicates that the CEO may have had something to hide. Enron
failed soon thereafter.
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Is management incentivised to focus on shareholder interests?
Executive managers that are paid with performance bonuses, shares and share options will
be incentivised to act in the interests of shareholders. We need to qualify this however, by
stating that share options may lead management to take on additional risks that may not
be in line with shareholders’ interests. This is because option holders have only the upside.
Therefore, it may pay management to take on more risky projects as they will not share in
any losses. However, there could be reputation risk from incurring losses. We will cover
options in Chapter 18.
Is the quality of management superior to other companies in the sector?
Quality of management is an important criterion for investing in a company, although this is
often reflected finally in the financial ratios. Management quality is indicated by the quality
of strategic, operating and financial decisions taken by management.
Does the company make optimal use of Information Technology?
Successful companies make optimal use of IT to manage sales, inventory and operations.
Companies such as Shoprite, Truworths and Edgars use IT extensively to manage inventory
not only from a control perspective, but to determine sales patterns and link this back to
production and procurement and to efficiently manage millions of transactions and accounts.
Edgars uses IT to manage over 3m customer accounts. We should evaluate a company’s
investment in IT and the performance of the IT function. Have there been any reports of
system break downs?
Does the company have valuable intangible assets?
Intangible assets include the quality of management, the quality of the people, the
training of personnel, advertising, research and development capabilities, innovation,
management of the supply chain, inventory management practices, IT capabilities and
customer service. Companies will often expense costs relating to these items and yet they
are hidden assets.
There are other factors to consider in specific situations. When companies undertake
mergers then it is important to undertake due diligence procedures. We expand on this
in Chapter 17.
FROM THE REAL WORLD …
Companies, analysts and credit rating agencies such as Standard & Poor’s use ratios extensively
to analyse the credit quality of companies. It is interesting to note which ratios are relevant in
each industry sector. For example, the gross profit and net profit margins, as well as inventory
turnover ratios are critical in the retail sector.
Standard & Poor’s
Standard & Poor’s is a leading credit rating organisation which provides information on the
creditworthiness of companies. Standard & Poor’s rates over US$11 trillion in bonds and other
financial obligations of companies operating in over 50 countries. The following are some of the
more relevant ratios that Standard & Poor’s uses to determine a company’s rating and which has
a major impact on the cost of debt financing for firms:
Financial_BOOK_2018_new.indb 41
EBIT interest coverage
Long-term debt/capital
EBITDA interest coverage
Total debt/capital
Funds from operations/total debt
Return on capital
Free operating cash flow/total debt
Operating income/sales
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Dun & Bradstreet
Dun & Bradstreet is a major credit rating agency and the company focuses on the following
solvency, efficiency and profitability ratios when analysing companies:
Solvency
Efficiency
Profitability
Quick ratio (acid test or liquidity)
Current ratio
Current liabilities to Net Worth1
Total liabilities to Net Worth
Fixed assets to Net Worth
Collection Period Ratio (days)
Sales to Inventory
Assets to Sales
Sales to Net Working Capital
Accounts Payable to Sales
Return on Sales (%)
Profit Margin
Return on Asets
Return on Net Worth (ROE)
1
Net worth is equivalent to shareholders equity
Sectoral ratios for South Africa
Table 5.9 Sectoral ratios in South Africa
The banking sector is not included in Table 5.9 owing to the nature of the sector. Important
ratios in the banking sector are the percentage of non-performing loans, the return on assets,
and the return on equity, the interest margin and the cost-to-income ratio.
SUMMARY
In this chapter we have discussed the main methods used to analyse the financial statements
of a business. Financial analysis is designed to determine the relative strengths and
weaknesses of a firm. To do this it is necessary to get some benchmark which is normally
based on either historic performance or on how other firms within the same industry
perform.
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Investors need financial information in order to estimate both future cash flows from the
firm and the riskiness of these cash flows. Managers need to be aware of their firm’s financial
position in order to detect its strengths and weaknesses so as to enable decisions that will
maximise shareholders’ wealth. The most popular approach to financial analysis is through
the use of ratios.
Ratios fall into six broad categories; liquidity, asset management, debt management,
profitability, cash flow, and market ratios. The ratio analysis procedure is as follows: calculate
a ratio, compare it with the previous ratios to establish if there is any trend, and/or to
compare it with those of other firms in the same industry to judge the relative strength of
the firm in question. If a structured system of analysis is used, such as the Du Pont system,
the interrelationship of ratios will help identify the cause of a weakness that is discovered.
While ratio analysis does have some limitations, if it is used perceptively these limitations
will not negate the effectiveness of the analysis.
EVA is a measure of performance that deducts an appropriate charge for the opportunity
cost of all capital invested in an enterprise from net operating profit. As such, EVA is an
estimate of true “economic” profit, or the amount by which earnings exceed or fall short of
the required minimum rate of return that shareholders and lenders could earn by investing
in other securities of comparable risk.
GUIDANCE ON FINANCIAL ANALYSIS
By Johnathan Dillon M.Com CA(SA)
Evaluating the performance of a firm is far broader than merely calculating financial statement
ratios and commenting thereon. There are many other important considerations, some of
which are covered in this section. Nonetheless, ratio analysis remains an important element of
broader performance evaluation and some useful pointers are provided below:
Pointers on ratio analysis
It is crucial to note the following in relation to the calculation and interpretation of financial
statement ratios covered in this chapter:
■■ Du Pont analysis: Prior to performing all possible ratio calculations for the various
categories of ratios, it is very useful to utilise the Du Pont model and calculate a few key
ratios. This provides a high-level overview of performance and insight into where further
investigation and ratio calculations are necessary.
■■ Consistency: When comparing and interpreting ratios, it is essential that the ratios be
calculated consistently between firms or across financial years.
■■ Context: Calculating ratios in isolation is largely meaningless – ratios are better
understood within the context of information relating to the firm and its industry.
Besides news sources, context is often obtained by reading the firm’s integrated report,
sustainability report or notes to the financial statements.
■■ Comparison: The analysis of ratios and performance is improved when compared to
targets/budget, prior years, benchmarks or another firm, whether in the same or similar
industry. Comparing the various ratios calculated is also important to identify possible
links, causes and consequences.
■■ Average balances: If relevant information is available then, depending on the ratio, it is
generally more correct to calculate ratios using average balances relating to amounts
disclosed in the firm’s statement of financial position. Examples include return on equity
(net profit after tax divided by average equity), average collection period (average
accounts receivable divided by credit sales per day) and asset turnover (sales divided
by average operating assets). Instances in which this would not be appropriate include
liquidity ratios and debt management ratios where the analysis is at a specific point in
time, namely, the end of the financial year.
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Movements and other percentage calculations: As noted in this chapter, ratio analysis is not
the only tool that can be used to analyse financial statements. It is often very useful to
calculate the percentage changes (movements) in amounts from one year to another. In
addition, calculating significant costs as a percentage of sales or total costs is also useful.
These percentages aid in identifying trends and potential problems (for example, accounts
receivable increasing at a greater rate than sales). They are also useful as they provide
greater context within which calculated ratios can be interpreted.
Further insights into broader performance evaluation
Over and above the financial statement analysis techniques discussed in this chapter, broader
performance evaluation of a firm encompasses many facets. A number of key concepts related
to broader performance evaluation are briefly covered below:
■■ Strategy: Performance should be compared to the firm’s long-term strategic plan, that is, is
the firm on track to achieve its long-term goals (mission and vision)? Performing a SWOT
analysis (an analysis of its strengths, weaknesses, opportunities and threats) and analysing
the industry’s profitability (using Porter’s five forces) will also aid in determining whether
the firm is performing well considering its circumstances.
■■ Growth: Growth is an important concept in relation to performance evaluation and is
often a sign of success. There are numerous ways of measuring growth, such as growth
in revenue, profitability, ROCE, market share, number of products and cash flow from
operations. When focusing on conventional ratio analysis calculations, these pertinent
growth calculations are easily omitted. Growth is not always a positive sign, especially
excessive growth, which could be an indication of overtrading and looming bankruptcy or
takeover.
■■ Cost management: Analysing costs is also a vital consideration when evaluating
performance, most notably containing or reducing operating costs. However, it is
often necessary for a firm to increase expenditure (such as marketing costs or research
expenditure) in order to increase sales volumes or innovate. Therefore, cost cutting is not
always a good sign.
■■ Break-even analysis and capacity: Besides being an indicator of business risk, calculating
a firm’s break-even level of sales (and margin of safety) is invaluable as it provides an
indication of whether the actual level of sales is satisfactory. Furthermore, knowing
a firm’s practical capacity level is helpful when analysing performance as it indicates
whether a firm can in fact break even (if not yet at that point). It also indicates the
potential upside if demand increases or the need to increase capacity in the near future
which may require a substantial capital outlay.
■■ Non-financial factors: Performance evaluation must not focus solely on “the numbers”
(financial performance) but should also analyse how the firm is performing in relation
to its customers, operations, employees, infrastructure development (non-financial
performance), and so on. Performance can therefore also be measured in relation to the
expectation of various stakeholders. However, shareholders remain the most important
stakeholders that the management of a profit-orientated firm should predominantly focus
on.
■■ Long-term focus: It is important to not only have a short-term focus when evaluating
the performance of employees, as this could impact negatively on their behaviour and
the long-run performance of a firm. Performance measures that result in a short-term
focus include ROCE and other profitability ratios. For example, management may delay
necessary capital investment in order to keep the ROCE ratio high in the short run. In
such instances, it is recommended that the period over which performance is measured be
lengthened beyond one year in order to avoid a short-term focus.
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S
SELF-STUDY PROBLEMS
S5.1
Barrax Limited has the following Statement of Financial Position (balance sheet) at the end
of 20x5. The current liabilities include short-term interest bearing debt of R10 million. The
company has 10 million ordinary shares in issue and the current share price is R8.20.
What is the company’s debt to equity ratio? What is the company’s market capitalisation?
What is the company’s debt to market capitalisation ratio? What is the company’s current
ratio?
S5.2
Ukhosi Ltd has R18 million in inventories and this represents 2 months sales. What is the
company’s inventory turnover ratio (sales/inventory)?
S5.3
Dome Limited is an industrial holding company. Extracts from the company’s latest annual
Financial Statements are as follows:
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Required:
Calculate all the relevant ratios for Dome Limited as at 30 June 20.2 and 20.1.
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Solutions to Self-study problems
S5.1 Solution
1. Total debt = Long term debt + short-term debt = R50m + R10m = R60m
Debt to Equity = 60/60 = 100%
2. Market capitalisation = share price × number of shares in issue = R8.20 × 10m
= R82m
3. Debt to market capitalisation = 60/82 = 73%
4. Current ratio = current assets/current liabilities = 40/30 = 1.33
S5.2 Solution
Sales = [inventory/no. of months sales] × 12
Sales = (18/2) × 12 = R108m
Inventory turnover (sales/inventory) = 108/18 = 6
S5.3 Solution
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APPENDIX 5.1 SUSTAINABLE GROWTH
Introduction
The rationale for growth requires that companies achieve a superior return on assets.
However, the return on the assets is only one of the factors affecting growth. The company’s
financial policies must be of a nature that permits the company to take advantage of growth
opportunities. These financial policies dictate the level of sustainable growth.
The determinants of growth
Growth is possible, firstly, if there are growth opportunities and, secondly, if the company’s
financial strategies are structured to allow the company to grow.
Return on assets
A company can grow at the rate of return on its assets if it does not pay any dividends and is
not financed from outside sources – i.e. if it is entirely financed by shareholders’ funds. Let us
examine this.
Example 5.1: Return on assets
Company A has assets of R1 000m and earns 20% on those assets. It can therefore grow at
20%. Assume it has 100m shares of R10 each. Assume also that assets are reflected at market
values.
Assets
Shareholders’ equity
Value per share R
Beginning of year
End of the year
Rm
Rm
1,000
1,000
R10.00
1,200
1,200
R12.00
The growth rate has been the return on assets, which is based on EBIAT.
Dividend policy
Note that we imposed certain limiting assumptions on our company, namely there was no
outside finance nor was there any dividend. Let us now introduce the payment of a dividend.
Example 5.2: Dividend policy
Assume company A pays a dividend of 25% of its earnings.
Return on assets after tax
Dividend
R200m
R50m
Assets at end of year
R1,150m
Shareholders’ equity at end of year
R1,150m
The growth has been the return on assets that have been retained in the company. As there is no
financial leverage, the ROA is equal to the firm’s ROE. This may be expressed as:
Sustainable growth rate = Rp
where: R = percentage return on assets after tax
p = proportion of earnings retained
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Applying this to company A:
SGR = 20 × 0.75
= 15%
Company A can grow earnings at a rate of 15%.
Capital structure
Let us now introduce some external financing.
Example 5.3: Capital structure
Assume that company A is financed 60% by equity and 40% by debt bearing interest at 10%
per year. The company’s Statement of Financial Position at the beginning of the year will
therefore appear as follows:
Statement of Financial Position
Rm
Equity600
Debt400
1,000
Assets1,000
Net income after tax (20% of assets)
Interest on debt: 10%
40
Tax shield on interest (t = 30%)
-12
Net profit
Dividend
25%
Retained earnings
200
28
172
43
129
The company can grow by its retained earnings of R129m [(which is a growth rate of 12.9%
(129/1000)]. In addition it can raise further finance against the R129m in the target debtequity ratio which, in this case, is 4:6. Therefore it can raise debt of R86m. Assets will grow to
R1 215m (by 21.5%) financed by R729m (600 + 129) in equity and R486m (400 + 86) in debt.
This may be expressed as follows:
__
D
SGR = ​   ​(R – i)p + Rp(Formula 5.4)
E
where: R = percentage return on assets after tax
p = proportion of earnings retained
D = debt
E = equity
i = percentage interest rate on debt after tax
Applying this to the above case:
____
400
SGR = ​   ​(13%) × 75% + 20% × 75%
600
= 21.5%
Note that the growth determined logically above amounted to R215m which is 21.5% of
R1 000m. This formula is often referred to as Zakon’s formula.
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With this formula, as with any other ratio, care must be taken to ensure that the terms used
are internally consistent. In this case, if the return on assets is regarded as return on net assets,
the debt should be long-term debt and the interest rate the average rate on that debt, whereas
if the return on assets is the return on total assets, total debt and the average rate of interest
thereon should be used.
Summary
The determinants of growth are:
■■ the return on assets;
■■ the interest rate on debt;
■■ the debt-equity ratio; and
■■ the retained earnings ratio.
If a company wants to grow it needs to consider these parameters.
Given that its investment opportunities (R in the formula) permit the growth, the company
then has to arrange its financial policies in such a way as to make the growth possible. This can
be done either by increasing the debt ratio or by reducing the dividend payout. The company
does not usually have much influence over the interest rate.
Example 5.4
Zak is in an industry in which the typical growth rate is in the region of 12% per year. The
following details apply to Zak:
■■ Return on assets
15% (after tax)
■■ Debt-equity ratio
4:6
■■ Interest on debt
10%
■■ Dividend policy
70% payout
■■ Tax rate
30%
Suggested solution
__
4
SGR = ​   ​ (8%) × 30% + 15% × 30%
6
= 6.1%
Note: 8% = 15% – (10% × 0,70)
Given the financial policies adopted by Zak, it cannot match the growth in the industry. The
primary cause of the low growth in this case is the abnormally high dividend payout. A 12%
growth could be achieved if the dividend were to be reduced.
__
4
12% = ​   ​(8%) × p + 15% × p
6
p = 59%
Thus a growth rate of 12% could be sustained if the earnings retained were 59% or, in other
words, if the company changed its dividend policy to paying out only 41% of its earnings.
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APPENDIX 5.2 THE THREE MOST CRUCIAL RATIOS IN EQUITY ANALYSIS
Zwelakhe Mnguni is the Chief Investment Officer and co-founder of Benguela Global
Fund Managers. He has over 15 years of investment experience. Most recently Zwelakhe
spent 3 years as Head of Equities and Portfolio Manager at Mergence Investment
Managers (Pty) Ltd, where he successfully managed the equity mandates for clients.
Prior to Mergence, Zwelakhe was Portfolio Manager and Equity Analyst at Stanlib,
where he managed the Global Science and Technology Fund as well as co-managing
the Stanlib Value Fund. Prior to this he spent 4 years at Allan Gray as an Equity
Analyst. Zwelakhe has an excellent record as a portfolio manager. Zwelakhe holds a
B.Com(Hons) degree in Financial Management.
Introduction
Finance theory teaches us that investing is about maximising returns and minimising risk. This
applies to capital allocation decisions in a business as well as to common share investing in
the primary/secondary capital markets. While the principle is important across all primary asset
classes like equities , bonds, real estate and cash, it is crucial for equity investors because of too
many unknowns. In theory, all investors should only invest in a business if the potential returns
outweigh the most probable risks.
Unlike in fixed-income securities where the future value, investment maturity date and yield
on the underlying securities are known upfront, common equity securities have no maturity date,
no pre-set future value or a predefined investment yield. These unknowns elevate the risk profile
of equity investments relative to safe assets like bonds and cash. However, equity investors also
have potential to make the highest returns if their chosen investment performs. This is what is
known as the equity risk premium in finance.
Equity investors are recipients of the residual income/yield of a going concern and residual
value of assets in a dissolving business. In a going concern, equity investment finance theory
teaches us that the future value of a business is the present value of future cash flows discounted
at the appropriate risk-adjusted rate. The uncertainty around future cash flows is a major driver
of the discount rate applied on the most probable cash flow outcomes. On the other hand, the
future value of an equity investment in a dissolving business is the net realisable value of the
underlying assets less the current value of the liabilities. In a dissolving business the biggest risk is
that the recorded value of assets in the balance sheet is substantially lower than the net realisable
value (NRV). An even bigger risk in a dissolving business is that the NRV is not sufficient to
cover the current value of liabilities. This is what gives rise to business bankruptcy in which case
equity investors walk away with losing all their invested capital.
Most investors tend to approach equity investing from a return perspective and accept
whatever risk they are exposed to as secondary. My approach to investing is different in that
I prioritise risk analysis over return analysis. I believe being reckless on risk assessment and
sensible on return analysis is a recipe for disaster.
Below I discuss the three ratios without which I would never undertake equity investments.
They are grounded on the well-known but often neglected risk of investing in the equity asset
class. It is important that they be considered both on a historic and on a forward-looking basis.
The goal is to provide the reader with the absolute minimum arsenal towards risk minimisation
for equity investing.
Positive Free Cash Flow Margins
Free cash flows are key indicator of business health and a primary driver of value. As discussed
above, the value of a business is dependent on the expected future cash flows. Free cash flow
of the firm (FCFF) represents the cash that a company is able to generate after laying out the
money required to maintain or expand its asset base. It is arrived at after deducting from all
cash received from customers the cash paid to employees, suppliers and capital to maintain the
current operations.
Calculation: The FCFF = earnings before interest and taxes (EBIT also called Operating Profit)
plus depreciation minus cash taxes paid minus new investments in working capital minus capital
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expenditures to maintain operations. Calculation of FCFF Margin: Having calculated the FCFF
cash flow of firm
_______________
​  Free
​
above, the FCFF margin is simply the FCFF divided by Total Revenue i.e.
Total Revenues
Risk perspective on FCFF Margin: Accounting earnings can and have been manipulated
by companies in the past. A company that reports accounting profits but those profits don’t
translate into cash is generally a very risky investment. To lower the risk on their investments,
equity investors need to invest in businesses that consistently generate free cash flows. The more
consistent the FCFF margins the lower the financial risk a business may face in future. Without
consistently generating free cash flows, a business would sooner or later have to borrow from
debt providers or issue shares at possibly a highly dilutive price. Increased levels of debt increase
the risk of financial bankruptcy for any business. As a minimum we want consistently positive
FCFF margins and at best we want them high and stable.
Return perspective on FCFF Margin: a higher free cash flow margin does not only indicate
the health of a business, it is the base from which a business can declare dividends (a form of
yield for equity investors), buy back shares and pay down the debt. As a result, the consistency
of FCFF margins can be a good indicator of what investors can expect in future dividends. In
addition, high free cash flows should benefit valuations unless they are reinvested in lower return
operations of a firm.
Specimens from JSE Top 40 Index:
Table 5.10 shows examples from the JSE Top 40 Index with a five-year track record of positive
free cash flow margins.
Table 5.10 JSE Top 40 companies with a five-year track record of positive free cash flow margins
Source: Company Annual Reports, Benguela Global Research Analysis
FCF6 Return on Invested Capital (FCF-ROIC)
While the FCFF margin is an important measure of the health and cash profitability of a business,
we need to understand how much capital was invested into the business to enable it to generate
those free cash flows. Furthermore, it serves no value to capital providers that the business
generates substantial free cash flows but is unable to meet the expected return of investors. Free
Cash Flow Return on Invested Capital measures the quality of a business in that it measures the
free cash flow generated by the business against all invested capital (including debt-financed
capital). Thus, FCF-ROIC enables us to compare the attractiveness of an investment in a share
relative to other alternative investment opportunities like bonds, cash or other shares.
Calculation: FCF return on invested capital is calculated as FCFF divided by Total Invested
cash flow of firm
_______________
​  Free
​
Capital i.e.
Total invested capital
FCF in this context refers to Free Cash Flow of the Firm (FCFF) but is often referred to as FCF in practice.
Therefore, we have retained the use of FCF here.
6
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Risk perspective on FCF-ROIC: From a risk perspective, calculating FCF-ROIC helps us
understand risk in the investment because it enables us to compare the returns we are getting
against other asset classes (bonds, cash or other shares) and our required returns. The higher the
FCF-ROIC above a benchmark asset or costs of capital, the better the quality of the investment
from a risk point of view.
Return perspective on FCF-ROIC: Companies that invest capital in high FCF-ROIC generating
opportunities are growing the value of that invested capital. The continuous compounding of
capital at a rate higher than the cost of capital means that the value of the shares should increase
in tandem with the excess of FCF-ROIC over cost of capital. This measure is superior to return
on equity, which can be manipulated through accounting entries and financial leverage.
Specimens from JSE Top 40 Index:
Table 5.11 shows examples from the JSE Top 40 Index with a five-year track record of FCFROIC of 10% or more for five consecutive years.
Table 5.11 JSE Top 40 companies with a 5-year track record of FCF-ROIC of 10% or more for 5
consecutive years
s
Source: Company Annual Reports, Benguela Global Research Analysis
Net Debt to Tangible Net Asset Value (ND-to-TNAV)
One of the major weaknesses of applying finance theory is that it imputes the benefits of debt
from a lower cost of capital perspective but often fails to take into account the fact that as debt
levels increase, the financial risk also increases. A recent example from South Africa whose
effects have reverberated across the world is Steinhoff. Initially as debt increased, investors
discounted the Steinhoff free cash flows at a lower cost of capital. And when the issue of fraud
surfaced, investors were spooked by the high level of debt and marked the share price down by
over 95%.
One of the risks that flows from investing in equities as opposed to sovereign bonds, for
example, is the risk of bankruptcy. As discussed above, outside the operating environment
effects, the primary driver of bankruptcy risk is the level of indebtedness in a business. When the
company fails to pay its debts due to a liquidity crunch and faces liquidation, shareholders can
only hope that the net realisable value of assets is greater than the current value of liabilities.
Intangible assets like Goodwill, Trademarks and Patents are often difficult to sell in a dissolving
business and for that reason, we would be safe in comparing net debt to the tangible assets.
Preferably, net debt should be lower than 80% of net tangible asset value. This would leave
enough headroom for up to a 10% possible impairment of assets in a fire sale liquidation.
Calculation: Net Debt to Tangible Book (NAV) value is calculated as:
Total interest – bearing borrowings – Cash and cash equivalents
Total equity – Intangible assets
___________________________________________________
​
​
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Risk perspective on ND-to-TNAV: Aiming to invest in companies that have low levels of debt is
a major contributor to low financial risk. In cyclical industries it is imperative that debt levels be
kept in check given that a sudden cyclical downturn may leave a highly indebted business high
and dry from a cash flow point of view. This may force the company to sell assets at massively
discounted prices like we saw in the case of Aspen, which sold its Infant Milk Formula business
at a massive discount to market value due to debt pressures. Anglo American plc and Glencore
experienced the same issue in 2015. The effect of a forced sale of assets due to debt causes
permanent loss of capital for the businesses. As a result, keeping an eye on the level of debt
relative to the value of tangible assets could help us avoid the risk of capital loss.
Return perspective on ND-to-TNAV: Businesses own assets for the purpose of implementing
their strategies. When businesses have to sell assets to settle liabilities, the going concern value
decreases and is reflected in the share prices. So the sale of assets to settle debt could be a very
negative signal to investors that things are falling apart from a going concern perspective. The
ND-to-TNAV ratio could serve as an early warning for what returns we could expect if things go
badly operationally.
Figure 5.3 Top 20 ranking companies by net debt to tangible NAV
[Source: Company Annual Reports FY2018 or 1H2018, Benguela Global Research Analysis]
Conclusion
Finance theory teaches us some valuable principles about investing and equity valuation.
Investing is about maximising returns and minimising risk. Also the value of a business is the
present value of its future cash flows. As investors in equity capital markets we need to remain
as close as we can to these fundamental principles and not get carried away by the low price
multiples like price-to-earnings and other fleeting factors. To conclude, I believe that investors
have to prioritise risk assessment ahead of expected returns given that expected returns are
not guaranteed. Investors should always ask themselves, if they are wrong on their return
expectations, what could they lose? The three ratios above are fundamentally linked to the
value and risk in a business. I believe that these should serve as minimum requirements prior to
making investment decisions for equities.
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APPENDIX 5.3 TRUWORTHS AND THE OUTCOMES OF THE SIX CAPITALS
Truworths sets out the outcomes of the six capitals in in its 2018 Integrated Report as follows:
Truworths also goes on to set out its actions to enhance or mitigate outcomes in 2018. We refer
you to the Truworths corporate website for access to its integrated report, www.truworths.co.za/
investors.
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Q
QUESTIONS
Question 5.1
ABC Limited is listed on the JSE. There are various stake-holders.
(a) As an existing shareholder, which ratios would you choose so as to monitor your investment?
(b) As a creditor providing goods to the company on credit which ratios would you analyse?
(c) As a lender of long-term loans to the company, which ratios would you use so as to safeguard
your money?
Question 5.2
Your company wishes to borrow money but does not want to over extend itself and become
vulnerable to changes in market conditions. Which ratios would be useful in analysing the extent
to which they can borrow? Would the industry averages be of any use and if so why?
Question 5.3
How does the Du Pont system of analysis identify the components of the return on investment?
How does this relate to the return on equity?
Question 5.4
What are the implications of using income before tax for the analysis of profitability? What are
the implications of using income before interest and taxes for this purpose?
Question 5.5
Certain rule-of-thumb ratios exist – for example, a current ratio of 2:1 or quick ratio of 1:1. What
purpose do these rule-of-thumb ratios serve?
Question 5.6
What are the most serious limitations of the use of industry averages in ratio analysis?
Question 5.7
Redrack Ltd operates in the retail sector. The company has experienced tough trading conditions
in the last year. The company’s net profit margin was 3% and the company achieved an asset
turnover of 1.7. The company’s debt-equity ratio is 40%.
Required:
(a) What is the company’s Return on Assets (ROA)?
(b) What is the company’s Return on Equity (ROE)?
(c) Assume that the company expects to experience an increase in its net profit margin to 10%
and its asset turnover is expected to be 2.5 in the coming year. The company’s debt-equity
ratio will be 66.67%. What effect will these changes have on the company’s ROE?
Question 5.8
Tryon Ltd is a clothing manufacturer that also operates a chain of clothing stores. The company’s
debt consists of bank loans amounting to R8.5 million and the company’s sales revenue is R32
million per year. The company is currently earning a net profit margin after tax of 8% per year.
The corporate tax rate is 28% and the company is paying an interest rate of 9% per year (before
tax).
Required:
What is the times-interest-earned ratio? How will this change if the company’s net profit margin
falls to 6% and the interest rate rises to 10% per year?
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Question 5.9
Ukuza Ltd has appointed a new CEO due to experiencing lower returns in the past year. Its
ROE had fallen to 8% for the first time in its history. The company expects its operating income
(EBIT) to be R12 million and sales revenue is expected to be R80 million for coming year.
The company’s asset turnover is expected to be 1.6 times and the company is expected to pay
R2 million in interest on a debt level of R25 million. The asset turnover is on the basis of noncurrent assets plus net working capital. The corporate tax rate is 28%.
Required:
(a) What is the company’s expected debt-equity ratio?
(b) What is the company’s expected ROE?
Question 5.10
Stax Ltd is a listed company which has produced the following summarised Statement of
Comprensive Income and Statement of Financial Position for the year ended 30 June 20x5.
Required:
(a) What is the debt-equity ratio?
(b) What is the interest cover (times interest earned)?
(c) What is the total asset cover? What is the fixed asset cover?
(d) What is the company’s net profit margin?
(e) What is the operating return on assets?
(f) What is the return on equity (ROE)?
(g) If the company’s cost of capital is 11%, what is the company’s EVA?
(h) Assume that the company’s market capitalisation is R52.5m and the company has 7 million
shares in issue. Determine the company’s earnings per share (EPS)? What is the company’s
price–earnings (P/E) ratio? How does this compare to the average for the JSE of 16?
Question 5.11
Umklomelo Ltd has the following Statement of Financial Position at the end of 20x5. The current
liabilities include short-term interest bearing debt of R40 million. The company has 100 million
ordinary shares in issue and the current share price is R12.00.
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Required:
(a) What is the company’s current ratio?
(b) What is the company’s debt-equity ratio?
(c) What is the company’s market capitalisation?
(d) What is the company’s debt to market capitalisation ratio?
Question 5.12
Instax Ltd is a company involved in the production of auto components. The following
information is extracted from the company’s financial statements for the years ending
30 June, 20.7 and 30 June, 20.6.
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Required:
Comment on the company’s liquidity position and the company’s management of working capital
in 20.7 as compared to 20.6 based on the relevant ratios.
Question 5.13
The following statistics have been extracted from the five most recent years’ annual financial
statements of Jules Ltd, a manufacturing company engaged in the footwear industry.
Years ended 30 June:
20.2
20.3
20.4
20.5
20.6
Ratios
Profit before tax: to capital employed
12.0%
12.8%
9.6
6.9%
2.5%
6.0%
5.8%
5.3%
5.7%
2.8%
2.0×
2.2×
1.8×
1.2×
0.9×
0.9
0.8
0.9
0.7
0.5
7.0×
6.8×
7.6×
9.1×
12.1×
Retained profit: to shareholders’ funds
14.9%
17.9%
18.2%
20.3%
9.5%
Retained profit: to operating profit
20.0%
20.9%
16.7%
17.8%
8.3%
2.3×
2.2×
1.7×
1.7×
1.3×
Profit before tax: to sales
Sales: to capital employed (net assets)
Current ratio
Total debt: to shareholders’ funds
Interest cover
Index Numbers: Jules Ltd
Sales
100
122
179
215
262
Profit before tax
100
118
159
205
123
Fixed assets
100
125
189
362
590
Total debt
100
116
159
238
348
Long-term debt
100
107
221
431
735
Notes
1. No new issues of shares were made during the period.
2. Dividends remained constant throughout the period.
3. The ratio of long-term debt to shareholders’ funds at 30 June, 20.2, was 2.5:1.
Required:
Comment briefly on the circumstances under which these figures might reflect good or bad
financial management of the company.
(CIMA)
Question 5.14
The following ratios have been extracted from the financial statements of a company listed on
the JSE under the general retailers sector. For comparative purposes the sector ratios are also
shown.
Company
Sector average
20.5
20.4
20.5
20.4
Current ratio
0.81:1
0.86:1
1.68:1
1.58:1
Quick (acid-test) ratio
0.30:1
0.17:1
0.60:1
0.55:1
Debt ratio
0.668
0.640
0.510
0.517
Interest cover
33.32×
31.10×
6.87×
7.83×
Fixed charge cover
11.01×
10.23×
4.93×
5.51×
1.49:1
1.38:1
1.11:1
1.17:1
Fixed assets to owners’ equity
Sales to owners’ equity
Net income after tax
Earnings per ordinary share
Book value per ordinary share
Financial_BOOK_2018_new.indb 59
15.11:1
14.49:1
9.01:1
9.71:1
Up 6.5%
Up 14.2%
Down 3.1%
Up 3.2%
–
–
171.2c
160.8c
Up 16.6%
Up 30.1%
Up 4.1% Up 15.2%
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Required:
(a) Prepare a list of comments stating how each of the above items indicates how profitable the
company is and how each of the above items indicates what the future prospects are likely
to be. The implications of each ratio should be given separately and then the collective
inference that may be drawn should be given.
(b) What warnings should you offer about the limitations of ratio analysis for the purpose stated
here?
Question 5.15
At the end of 20.3, the assets and profit of Division S (part of a group) were as follows:
Rm
Fixed assets (book value)
Net current assets
Assets (capital employed)
EBIT
300
40
340
64
The fixed assets of Division S consist of land (R120m) and five separate items of plant and
equipment each costing R60m which are depreciated to zero over five years on a straight-line
basis. For each of the past years, on 31 December, it has bought a replacement for the asset
that has just been withdrawn and it proposes to continue this policy. Because of technological
advances the asset manufacturer has been able to keep his prices constant over time. The group’s
cost of capital is 15%.
Required:
Assuming that, except where otherwise stated, there are no changes in the above data, you are
required to deal with the following separate situations:
(a) Division S has the opportunity of an investment costing R60m and yielding an annual profit
of R10m.
(i) Calculate its new Return on Assets (ROA) if the investment were undertaken.
(ii) State, with brief reasons, whether you would recommend that the investment be
undertaken.
(b) Division S has the opportunity of selling, at a price equal to its written-down book value of
R24m, an asset that currently earns R3.9m p.a.
(i) Calculate its new ROA if the asset were sold.
(ii) State, with brief reasons, whether you would recommend the sale of the asset.
(c) Assuming that over the past four years the cost of Division S’s total fixed assets has increased
by 10% p.a. but that its EBIT has only increased by 6% p.a., calculate its ROA for next year
if inflation now ceases.
(d) Assuming that Division S decides to spend R6m p.a. on special promotional campaigns each
of which will yield an EBIT of R2m p.a. for five years, calculate its ROA at the end of the
fourth year (20.7) on the basis of the campaign expenditure being:
(i) charged as a cost of the period;
(ii) capitalised and amortised over five years.
(CIMA)
Question 5.16
As the management accountant for a group of four similar companies, you have recently
introduced an interim comparison scheme. A summary of basic information received from each
company for the period under review is given below and you are required to:
(a) present the information to management in such a way as to compare clearly the results
achieved by each company with those of the rest of the group; and
(b) write a short constructive report to the directors of company A, setting out the possible
reasons for the differences in their results as compared with the rest of the group.
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FINANCIAL STATEMENT ANALYSIS
Companies
A
B
C
D
Rm
Rm
Rm
Rm
Operating profit
221
209
315
162
Current assets
520
385
525
315
Fixed assets
930
715
975
585
Sales
2,470
1,980
2,925
1,665
Production cost
1,605
1,228
1,784
1,016
Selling cost
370
317
497
300
Administration cost
274
226
329
187
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(CIMA)
Question 5.17
The comments below were by different people looking at the same set of published accounts.
You are required to give your opinion on the statements made.
(a) The quick ratio is below the norm of 1:1 so the business:
(i) is technically insolvent;
(ii) is suffering a liquidity crisis; and
(iii) probably need not take any corrective action.
(b) Each R100 of total assets is financed by R37.50 debt and R62.50 equity. The business:
(i) should borrow more money, because the ratio of debt to total assets is too low; and
(ii) must not increase its borrowing because the debt-equity ratio is above 50%.
(CIMA)
Question 5.18
Three companies in the same business risk category produced the following abbreviated results
for the financial year ended 31 March, 20.1:
Ordinary shareholders’ equity
Propcor
Tecfin
Sadev
Rm
Rm
Rm
640
230
390
16% Mortgage bond
120
–
–
18% Long-term loans
102
55
318
862
285
708
Propcor
Tecfin
Sadev
Rm
Rm
Rm
Fixed assets
684
260
494
Net working capital
178
25
214
Inventory
319
263
612
Debtors
204
28
154
Cash resources
Overdraft and creditors
Net operating income
Interest
51
109
(396)
(375)
(552)
862
285
708
353
185
250
90
10
58
Net income before tax
263
175
192
Taxation
126
84
92
Net income
137
91
100
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Required:
(a) For each company, calculate three different measures (expressed as a percentage) for return
on assets. Please define each measure clearly.
(b) Comment briefly on the comparative performance of the companies in achieving return on
assets.
Question 5.19
The consolidated Statement of Comprehensive Income and Statement of Financial Position of
the Ikhwezi group for the year ending 30 September, 20.8 are given below:
The Ikhwezi group is involved in the manufacturing and marketing of packaging products and
printing paper and related products.
The price of each ordinary share at year end was R25.50 and there were 46 759 000 ordinary
shares in issue. The total market value of the preference shares (included in share capital)
amounted to R1m.
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Required:
(a) Using ratio analysis, comment on the group’s liquidity position, its debt and asset management
and profitability performance in 20.8 as compared to 20.7.
(b) Apply the Altman failure prediction model to Ikhwezi’s data in 20.8 to assess the likelihood
of corporate failure.
Question 5.20
Shadeports Limited operates in the home and office improvements industry. The company
constructs carports and protective structures for motor vehicles in homes, large office blocks,
and factories. The company was launched 15 years ago by an entrepreneur, Robbie Phelps. It
developed through aggressive marketing and has branches throughout South Africa. It obtained
a listing on the main board of the JSE in 20.8. The summarised Statement of Financial Position
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and Statement of Comprehensive Income for the financial year ended 31 December, 20.11, have
been obtained for analysis.
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Industry ratios for 20.11:
■■ Current ratio2:1
■■ Acid test (quick ratio)1:1
■■ Inventory turnover (sales/inventory)
6×
■■ Accounts receivable collection period
40 days
■■ Debt ratio50%
■■ Times interest earned6×
■■ Net income before interest and tax/total assets
17%
■■ Return on ordinary shareholders equity
21%
Required:
(a) Compute the relevant ratios for 20.11 and 20.10 required for an analysis of the company’s
liquidity position and management of current assets. Comment on your findings.
(b) Compute the relevant ratios for 20.11 and 20.10 required for an analysis of the company’s
use of debt to finance its operations. Comment on your findings.
(c) Compute four profitability ratios, two of which will provide information regarding the
operating effectiveness, and two of which will assist in establishing the effectiveness of the
use of assets. Comment on the selection of the ratios which you consider appropriate and the
information which they provide.
(d) Compute the return on shareholders’ equity based on book values and compare this with
market indicators of return. Comment on the differences and explain the relevance of each
figure calculated.
(e) Identify the additional information which may be available if a Statement of Cash Flows is
prepared and explain how this may assist in your analysis.
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Question 5.21
XYZ Brewing (Pty) Ltd is in the business of manufacturing and selling beer. Its two major brands
are Don and Skok. The company is very old and established and for many years has operated
from the original main plant. At the beginning of its 20.6 financial year, the company purchased
a second plant which was owned by a family business. This plant consisted of a brewery and a
can-manufacturing operation, together with extensive inventory and other assets. Certain of the
major assets were revalued in determining the purchase price. XYZ Brewing (Pty) Ltd paid cash
in settlement of the price agreed upon for the purchase of all the assets.
The company has grown satisfactorily during the last few years. One of the reasons for the
growth in sales is the policy of granting more favourable credit terms to distributors than its
three main competitors. You have been approached by a client who is considering investing in
XYZ Brewing (Pty) Ltd. She has provided you with Statements of Financial Position (balance
sheets) and Statements of Comprehensive Income (income statements) for the last five years.
Prior to your assessment, one of your employees has prepared financial statements expressed in
percentage terms, calculated certain ratios and obtained industry statistics. The information is
set out below.
Required:
(a) Evaluate the financial statements of XYZ Brewing (Pty) Ltd with particular attention to
liquidity, capital structure, profitability and turnover.
(b) State the advice you would give your client and list any additional information you would
require before making a firm recommendation.
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FINANCIAL STATEMENT ANALYSIS
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Question 5.22
Instead of using a single ratio or univariate analysis, Altman used a multivariate approach in order
to predict corporate failure. Altman analysed a range of financial ratios and their interactions to
devise a failure prediction model based mostly on accounting data.
Despite the successful predictive ability of this type of failure prediction model, which is
based on a sophisticated type of ratio analysis, the model is nevertheless subject to the same
limitations as conventional ratio analysis.
Required:
Explain the limitations underlying ratio analysis, and indicate how Altman’s failure prediction
model overcomes any of these limitations.
Question 5.23
Pipa Stores Limited, a public company listed on the JSE, has been engaged in the mass retailing
of food and other consumer goods for twenty years. During this period the company has displayed
consistent growth as evidenced by the increase in its total assets and earnings.
Since opening, the number of outlets increased from three to the current 94, employing
nearly 19 000 people. In the last 10 years the five-yearly compounded earnings growth has only
once been below 25% with the average being in the region of 34%. However, growth is expected
to decline and further estimates suggest that an expected compounded growth of 20% is feasible
and realistic due to international expansion. The shares trade at a PE of 15x.
The abridged financial statements are as follows:
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Required:
Compute and comment on what you consider to be the most relevant ratios. Use the Altman
failure prediction model to assess the likelihood of corporate financial distress.
Question 5.24
Supremo Tankers (Pty) Ltd (“Supremo”) operates a fleet of trucks and trailers to provide logistical
services to brick manufacturers in Gauteng and Mpumalanga. These services mainly entail the
transport of bricks on behalf of brick manufacturers to their customers. Supremo owns 100 trucks
together with “flat-bed” trailers. These transport vehicles have loading equipment specially
designed to load and unload bricks. The logistical services are offered to customers on one of the
following bases:
■■ An annual contractual basis to transport bricks from the brick manufacturer’s premises to
specified locations, based on a minimum number of loads per week. These contracts provide
for a fixed monthly charge subject to changes in diesel fuel prices. Contracts specify that
diesel fuel represents 20% of the total charge to customers and Supremo adjusts monthly
charges to customers with immediate effect in the event of a change in the retail price of
diesel fuel; or
■■ A per-load basis in terms of which Supremo charges an agreed transport fee per kilometer
travelled from the brick manufacturer’s premises to the delivery destination. These charges
also fluctuate depending on diesel fuel prices, based on the principle that diesel fuel costs
represent 20% of the total per kilometre charge to customers.
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The shareholders in Supremo are Sergio Parisse (70%) and BWI Holdings (Pty) Ltd (“BWI”)
(30%), which is a black economic empowerment investment company owned by three prominent
black businesswomen. Mr Parisse started Supremo 25 years ago and has been instrumental in
developing the business into the leading logistics provider to brick manufacturers in the provinces
in which it operates. Supremo focuses exclusively on services to brick manufacturers. Supremo’s
profitability has declined significantly in the 20.3 and 20.4 financial years, mainly because of lower
activity levels in the brick manufacturing industry. Research by an industry association revealed that
sales volumes of brick manufacturers were 25% lower in 20.3 than in the previous year, and that
sales volumes declined by a further 5% in 20.4. The decline in demand for its services that Supremo
has experienced has also had an effect on its capacity utilisation. Prior to 20.3 Supremo was able to
optimise load volumes and to ensure that it carried full loads on most occasions. This changed in
20.3 and now many of the trailers are empty on one or more legs of a journey. For example, bricks
may be delivered to a destination, but the trailer remains empty until the truck reaches the next
customer.
DAB Bank is the commercial banker to Supremo. DAB Bank has exclusively financed the
acquisition of trucks and trailers by Supremo over the past five years on an instalment sale basis.
DAB Bank requires a deposit of 20% of the purchase price of new vehicles when financing Supremo’s
acquisition of trucks and trailers. The instalment sale is repayable in equal monthly instalments over
six years and the capital outstanding bears interest at the prevailing prime overdraft rate (currently
10%). The bank overdraft balance with DAB Bank at 31 December 20.4 was R28 405 000. As a
result of the ongoing operating losses, DAB Bank has informed Supremo that they are required
to reduce their bank overdraft balance to R5 million by 28 February 20.5. If this overdraft balance
is not reduced, then DAB Bank will withdraw the overdraft facilities. Supremo has historically
adopted a policy of trading in or disposing of trucks after five years. Supremo has found that after
this period, trucks become very expensive to maintain and repair costs increase exponentially. This
does not apply to trailers as Supremo has workshop facilities where it overhauls and cost-effectively
maintains trailers to extend their useful life to more than ten years. The demand for used trucks has
declined dramatically over the past two years, which has had an adverse impact on disposal prices.
The strength of the rand has also had an impact on used truck prices. The trucks that Supremo uses
are imported and a strengthening rand has resulted in minimal price increases of new trucks, which
in turn affects the resale values of used trucks. Prior to 20.3 Supremo generally disposed of trucks
at prices that were higher than the carrying values. The financial results and financial position as per
the management accounts for the year ended 31 December 20.4 are set out below:
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Notes
1. Revenue declined by 10% in the 20.3 financial year compared to 20.2. Supremo did not increase annual or per
kilometre charges to customers in 20.3 and 20.4, except for changes relating to diesel fuel price fluctuations.
2. Details of the cost of sales are set out in the table below:
3.
4.
5.
Diesel fuel prices decreased on average by 35% during the 20.3 financial year. In 20.4, diesel prices increased
on average by 8%.
Operating and administrative costs are mainly fixed costs, with only 5% of these total expenses being variable
in relation to revenue and activity levels in the 20.3 and 20.4 financial years.
Supremo owns the property in Johannesburg from which it operates. The net book value and tax base of
land and buildings at 31 December 20.4 was R17 120 000. The property was acquired eight years ago for
R19m and a further R1m was immediately spent on refurbishing the premises. Buildings are depreciated
to a zero-residual value on a straight-line basis over 50 years (the depreciation charge for the 20.4 financial
year was R360 000). At 31 December 20.4 the net book value of the vehicle fleet was R139 300 000 (20.3:
R130 900 000).
Interest-bearing liabilities represent the balance outstanding on instalment sale agreements.
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Reduction of the bank overdraft
The shareholders of Supremo have met to discuss plans of action to reduce the bank overdraft to
R5m by February 20.5. BWI has indicated that it has no cash resources available to subscribe for
shares in Supremo or to advance a shareholder’s loan to the company. Mr Parisse has in principle
agreed to purchase the land and buildings owned by Supremo for R30m, which represents the
fair market value. He has furthermore agreed to lease the property to Supremo for five years at a
market related rental of R200 000 per month, subject to annual inflation escalations. The proceeds
from the sale of the property will be used to reduce the company’s bank overdraft.
Required:
a) Analyse and comment on the revenue and gross profit performance of Supremo in the 20.3
and 20.4 financial years. Calculate relevant ratios in support of your comments.
b) Identify and outline at least two possible actions that Supremo could take to return to
profitability on a sustainable basis and at least two possible actions that Supremo could take
to improve the cash flow generation of the business.
c) Critically discuss, from the perspective of Supremo, the proposed sale and leaseback of the
land and buildings.
(SAICA ITC/QE adapted)
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VALUATIONS
6
PRICING ON THE JSE AND VALUE: WHY EDCON USED VALUATION PRINCIPLES
TO GO PRIVATE
What does management do when it considers the market is undervaluing the company? This
was the question that the management of Edcon considered in 2007. Edcon was the largest
non-food retailer in South Africa with 32% share of the South African clothing and footwear
market yet management considered that the share price was understating the value of the group.
Management put in place an auction process whereby international private equity firms were
invited to tender for Edcon. Bain Capital bid R25 billion which was regarded as a high price for
Edcon. Bain Capital beat two other rivals for the group. The final offer represented a price of R46
per share which was 51% above the price of R30.40 per share that the company was trading on
the JSE before the announcement of buyout talks. The price was at a significant premium to the
JSE price. Why was this? The team at Bain Capital would have carefully valued Edcon on the
basis of discounted expected future cash flows and on the basis of EBITDA and P/E multiples.
Edcon appeared to be undervalued in relation to its international peers. Yet apart from Merrill
Lynch which valued the group at R46 per share prior to the buy-out, most analysts valued Edcon
within a range of R35 to R41 per share. The increase in value was expected to arise mainly from
the restructuring of the group as well as the value of tax shields arising from the issue of bonds
to finance the transaction. By 2014, it had become clear that the expected increase in operating
cash flows and savings used in the forecasts to justify the higher valuation had not materialised and
that any benefits from tax shields and leverage had been overstated. Edcon in 2014 was facing an
uncertain future. By 2017, Bain Capital’s equity was worth close to zero! Edcon’s balance sheet was
restructured and the lenders to Edcon became equity holders as there was no reasonable possibility
that Edcon would be able to repay its loans. At the time of writing in 2018, Edcon’s operating
performance remains under pressure. It seems that Bain Capital’s valuation at 46% above the
listed market price had been over-optimistic! Perhaps the market had got it right all along! In this
chapter, we will explore how to value bonds and we will analyse how to value companies on the
basis of discounted cash flows and price multiples.
LEARNING OBJECTIVES
After working through this chapter, you should be able to:
■■ Outline the concepts applied in the valuation of assets.
■■ Value debentures, bonds and preference shares using a discounted cash flow technique.
■■ Value ordinary equity using the dividend discount model.
■■ Employ the Free Cash Flow model to value the firm and the ordinary equity of a firm.
■■ Apply price multiples such as the price–earnings ratio to value ordinary shares.
■■ Employ the EVA approach to value ordinary equity.
■■ Adjust valuations for issues such as lack of marketability, share options and noncontrolling interests.
INTRODUCTION
In Chapter 2, we used time value of money principles to value bonds and debentures.
Although the valuation of preference shares is similar to the valuation of bonds, the
valuation of ordinary shares is much more challenging. Why is this? Bonds and preference
shares result in fixed income streams and so we can predict the future cash flows from such
securities. In the case of ordinary shares, this is much more difficult as ordinary shares will
result in cash flows which depend on many factors such as the state of the economy, the
actions of competitors, changes in currency rates, operating costs and the ability of the
company to grow market share.
In this chapter we will focus mainly on two methods of valuing ordinary shares; the
dividend discount model and the free cash flow model. We will also undertake relative
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valuations by using such indicators as price–earnings ratios (P/E) and market to book ratios.
Finally, we will use the EVA approach to value a company’s equity. We will apply what we
learn and value a real company.
1 VALUATION – AN OVERVIEW
In corporate finance, the valuation of any asset is determined by its future cash flows. The
value of any security is equal to the present value of the security’s expected future cash flows
discounted at an appropriate discount rate which reflects the underlying risk of such an
investment. An investment with uncertain cash flows will be valued less than an investment
which offers a greater level of certainty in terms of future cash flows. Investors need a
market to reflect trading prices. The JSE is a market that creates a listed price or value based
on the buying and selling interactions of millions of investors. As the future is uncertain
by definition, our estimation of future cash flows may be subject to error and yet we are
required to estimate future cash flows, discount cash flows and compare our value to the
listed share price. We should adjust our parameters and apply sensitivity analysis to our
valuation. Remember that although we may get to the wrong number we can still make the
right decision. Assume we value a company’s share price at R12, and the current listed price
is R8. Well, perhaps the real value is only R10 and so we got the wrong number but we made
the right decision to buy at the current price.
There are a number of valuation myths that we need to consider at the beginning:
■■ The valuation is quantitative and therefore correct. A value is usually expressed
quantitatively and may be the result of a formula or complex Excel model. As a result,
many often place an undue presumption of accuracy on the answer. Any combination
of inputs to the model will produce an answer; the important questions are what
informed the inputs, what assumptions were made, what was the purpose of the
valuation (e.g. a valuation for liquidation will likely be different from one for disposal
and again different from one for merger purposes), who are the parties, what are their
needs, what is their bargaining position, what is the size of the ownership?
■■ The valuation is objective. Valuations are influenced by the biases and needs of the
people performing them. Unintentionally the valuer may make assumptions which
generate an answer which satisfies a perceived need. For example, an equity analyst may
not want to be seen to be the odd person out and overestimate the growth potential of a
business. This was a common problem in the valuation of technology companies.
■■ The valuation has precision. Valuations are a function of estimates about future cash flows
and estimates of the cost of capital. Consequently even in the best circumstances they are
approximations.
■■ The valuation is valid over an extended time period. Since valuations are functions of
estimates about the future, as new information is received so the estimates of the future
change and the valuation changes. Estimates about the future would be influenced by
new information about the state of the economy, industry growth rates, interest rates
and currency rates.
■■ Only the answer matters. The answer can be important, but the benefit of carrying out a
valuation is that the rigorous process enables us to understand the fundamentals of the
business and what drives the value. It also uncovers the key variables on which the value
relies. This is particularly important, because if we know which variables influence the
value we can determine the sensitivity of the valuation to changes in those variables. Put
another way, we know what we’re betting on.
What are the fundamental building blocks of a valuation?
As the valuation of an investment is the present value of future cash flows, any valuation will
be affected by the following factors:
■■ The amount of each future cash flow;
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VALUATIONS
■■
■■
■■
6-3
The timing of such cash flows;
The riskiness of future cash flows; and
The required rate of return.
The amount and timing of future cash flows will be driven by the nature of the investment
and the management of such investments. The riskiness of future cash flows will depend
on the nature of the investment, and sensitivity to economic factors such as interest rates,
inflation and changes in currency rates.
The required rate of return (the discount rate) will be affected by a number of factors
such as the current government bond yield and the riskiness of future cash flows. We will
estimate the amount and timing of future cash flows and we will adjust the required rate of
return to take into account the riskiness of future cash flows.
2 THE EFFECT OF RISK AND RETURN ON VALUATIONS
The value of an item is inextricably bound to the return it generates and to the risk it
carries. This is true whether one is referring to monetary values and returns or simply to
benefits received. In this chapter we shall be concerned only with items whose value can be
expressed in monetary terms. In Chapter 2 we examined the mathematics of compounding,
discounting, and present value. We will now use these tools to value assets.
Example 6.1: Impact of return on value
Assume there are two assets: asset A yielding R1.0 million per year, and asset B yielding
R1.2 million per year. Assuming the risk is similar then clearly asset B is worth more than
asset A. We cannot, with the information supplied, say how much each asset is worth, but
we will agree that B is worth more than A, thus demonstrating that the return an asset yields
has a bearing on its value.
Example 6.2: Impact of risk on value
Now assume that there are two assets, C and D, each yielding R1 million per year, but asset
C is riskier than asset D. D is clearly worth more than C. Again we cannot place a value on
these assets but we do know that risk has a bearing on the value.
What, then, is needed to value the asset? All valuation models function on the
relationship between expected return and risk, and this is reflected in the required return
for that particular type of asset. If the expected return we receive on an asset, based on its
cost to us, is less than the return received on similar risk assets, then our asset is not worth
the price we paid for it.
Example 6.3: Valuation by comparing rates of return
R10 million
Cost of asset
Expected annual return
R1 million
Return on similar assets
12%
In this example it is clear that the asset is not worth R10m. This asset is returning only 10%
__
(​  1 ​), whereas it should yield 12%. An investor expects to receive a return of R1m by buying
10
an asset of similar risk, which yields a return of 12%, for less than R10m. Assuming a
perpetuity, then only R8.33m needs to be invested at 12% to earn a return of R1m.
3 REQUIRED RATE OF RETURN
Since the value of an asset is the present value of future cash flows, we need a rate at which
to discount our future cash flows. The determination of the required rate of return is thus a
crucial issue. It is the return that the investor requires, given the environment in which the
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FINANCIAL MANAGEMENT
investment is made. This can change at any time with changes in the expectations regarding
that environment. In some cases the rate is relatively easy to determine, particularly where
there are similar assets trading on the market.
For example, if the valuer wants to know the required return on a five-year debenture, it
is possible to identify other debentures of similar period and risk and determine their return.
However, the asset most frequently being valued is equity capital, and it is more challenging
to identify similar shares in order to observe the expected return. In such cases one needs
to try to establish the required return, given the particular circumstances pertaining to the
companies concerned.
The required return on a company’s shares is the cost of equity for those shares for
the company. Various models have been developed for calculating the cost of equity. The
calculation of the cost of equity will be covered in Chapter 7 using both the CAPM and
dividend growth models. We turn now to a consideration of valuation models for some of
the main categories of financial assets.
4 VALUATION OF DEBENTURES AND BONDS
We now revisit what we did in Chapter 2 when we used time value of money principles to
value debentures and corporate bonds. The valuation of fixed income securities such as
debentures, bonds and preference shares is relatively straightforward as these securities will
pay a fixed interest amount per period, which is usually on a semi-annual or quarterly basis.
When we value bonds, we need to understand some relevant terms. Par value refers to
the stated face value of the bond. Often bonds will be issued with a stated face value of
R100 and companies will normally issue and redeem bonds at this price. The company is
required to make fixed interest payments on bonds. These are known as coupon payments
and the payment divided by the par value is known as the coupon interest rate. There is no
relationship between the current market yield which changes day to day and the coupon
interest rate, except at the time of issue. Companies do sometimes issue bonds which may
pay a coupon interest rate for an initial period and then this becomes a variable rate of say
the JIBAR (Johannesburg Interbank Agreed Rate) quoted swap rate plus a premium of 2%.
Companies may also issue what is often termed as floating rate notes which are bonds that
pay a variable interest rate which may be issued at a premium to a rate such as the JIBAR
swap rate. There are other bonds which do not make any coupon interest payments; such
bonds are called zero coupon bonds. Bonds and debentures will normally have a maturity
date, or redemption date which represents the date that the bond will be redeemed. Yield
to maturity refers to the implicit return that an investor will earn by holding the bond or
debenture until maturity. This represents the market yield on a bond.
Debentures and bonds in perpetuity
A debenture in perpetuity has no redemption date and will continue indefinitely to pay
interest at the coupon rate. Such debentures are also known as non-redeemable bonds or
notes.
Example 6.4: Valuation of a bond in perpetuity
A non-redeemable bond has a face value of R100 and pays a coupon rate of 15% per annum.
The current market rate for similar bonds is 9%.
The value of the bond is clearly not R100. You will receive R15 (100 3 15%) every year,
and you should be getting R9 (100 3 9%). The required return may be said to be 9%.
Chapter 2 showed that the present value of an amount received in perpetuity can be
calculated by capitalising the return received at the required rate.
Value of the bond 5 R15/0.09
5 R166.67
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VALUATIONS
6-5
Redeemable debentures and bonds
A redeemable debenture has a maturity date on which redemption will take place. It cannot
therefore be capitalised in perpetuity.
There are two different types of cash flows involved in the valuation of redeemable
debentures. One is the periodic interest payment and the other is the repayment of the capital
at the date of redemption.
Example 6.5: Valuation of redeemable debentures (bonds)
A bond has a face value of R100 and pays an annual coupon interest rate of 15% per year,
and it is redeemable in five years’ time. Similar bonds have a market yield of 9%.
The interest is an annuity since the same amount is received each year. The present value
of the interest is therefore the annual interest discounted at the required rate of return,
which in this case is 9%. The discount factor used is that for an annuity at 9% for a period
of five years. Using Table D:
Present value of interest = R15 3 3.8897
= R58.34
To this must be added the value of the capital redemption. Since this is only to be received
in five years’ time it must be discounted for that period at the required return. The discount
factor used is that for an amount received in five years’ time at 9%.
Present value of capital = R100 3 0.6499
= R64.99
The value of the redeemable bond is therefore:
R58.34 + R64.99 = R123.33
Again we note that the value is higher than the face value since the actual return is higher
than the required return.
Using a Financial Calculator:
Using a financial calculator, enter the number for each variable followed by the function
key and then press the PV function for the answer. The answer represents the amount that
you would have to pay today for the future coupon payments and redemption of the face
value. We can depict the above bond’s cash flows as follows and use the Excel NPV function
to determine the value of the bond:
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We can see that a bond in perpetuity offering a coupon rate of 15% is valued at R166.67 as
compared to a bond which offers the same rate for 5 years, which is valued at R123.33. The
lower value reflects the fact that at the end of 5 years, investors will be required to reinvest
at the lower market rate of 9% per year.
The valuation of a redeemable bond may be expressed in general terms as:
n
Vd =

t51
_______
_______
I
P
​
​ 1 ​
​ (Formula 6.1)
(1 1 r)t
(1 1 r)n
where: r = required rate of return
n = number of periods
I = coupon payment per period
P = redemption of principal amount
If we are given a price for a bond or debenture, then the interest rate or discount rate that
makes the above formula true or valid, is the yield to maturity (YTM). Remember that this
is the same as the internal rate of return (IRR) and we can use the IRR function on most
financial calculators to determine a bond’s yield to maturity.
A bond may have a call provision which enables the company to call the bond or
debenture prior to its maturity date. For example, assume a bond is issued at a coupon rate
of 12% and the maturity date is in 10 years’ time. However, the company can call the bond
any time from year 5 until year 10. If the company calls the bond then the company may be
required to pay a premium above face value. We can then compute the yield to call. Why is
this important? Well, if market yields have fallen significantly, then it is probable that the
company will call in the bonds after 5 years and reissue at a lower interest rate. The return
that an investor will earn is probably the yield to call and not the higher yield to maturity.
In the above example, assume that the bond is currently trading at a price of R118. What
is the bond’s yield to maturity? We can use the IRR function on a financial calculator, or we
can use Excel as follows:
Using a Financial Calculator:
Using a financial calculator, enter the number for each variable followed by the function
key and then press the I/YR function for the answer. The answer of 10.2% represents the
interest rate that ensures that the sum of the present values of the coupon interest payments
and the redemption value equal the price of R118.
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FROM THE REAL WORLD … VALUATION OF ESKOM BONDS
Eskom has been issuing bonds in order to raise capital to finance the building of power generating
capacity. The ES23 bond offers a coupon rate of 10.0% per year with interest payable semiannually on 25 January and 25 July of each year. The redemption date is 25 January 2023. The
face value of each bond is R100. The ES23 bond is expected to offer a yield of 110 basis points
(1.1%) above the yield on a 5-year government bond, which was trading at a Yield to Maturity
(YTM) of 8.52%. This was also the yield on the R2023 government bond which matures in 2023.
What is the value of the bond on 25 July 2018?
The required return is 9.62%, which represents the government bond yield plus a risk
premium (8.52% + 1.1%). This rate translates to 4.81% per half-year and this is the discount
rate we have used to value the bond. The coupon payment due on 25 July would be paid to the
previous holder. We can set out the future coupon payments and the redemption payment in
Excel and determine the value of the bond by determining the NPV as at 25 July 2018, assuming
the next coupon payment will occur on 25 January 2019.
We can also use the Present Value tables or formulae to determine the present value of the
coupon payments which is an annuity and the present value of the maturity value which is the
face value of the bond.
As there is no accrued interest, the value in this case also represents the bond’s clean price. The
clean price is the value of a bond obtained by discounting all coupon payments (and the maturity
value) after the next interest payment date and excludes any accrued interest up to that date.
Therefore, on 25 July 2018, the clean price should be close to R101.36. If we determine what
the likely clean price will be on 25 January, it would be close to R101.24, which is the PV of the
coupon payments and the redemption value at that date (after the interest payment).
If we were valuing the bond on 21 September 2018, then we would need to add the accrued
interest to the bond’s clean price (at 25 July 2018) to get to the bond’s all-in price (also called
the bond’s dirty price). We will show you how to use Excel to value bonds in terms of the all-in
price and the clean price and then compare this to the quoted price reported by Sharenet as at
21 September 2018. To use Excel to value the bond as at 21 September 2018, you should use the
DATE and PRICE functions in Excel. The PRICE function in Excel enables us to value a bond
that pays periodic interest. The Excel function is as follows:
=Price(settlement, maturity, rate, yield, redemption, frequency, [basis])
Use the DATE function to enter the settlement and maturity dates. In this case we will set the
settlement date as 25 July 2018 in order to determine the clean price of the ES18 bond.
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The PRICE function in this case offers us the clean price of the bond. As you can see, this
agrees with our clean price calculation. If we were valuing the bond with a settlement date of
21 September 2018, then we would add accrued interest which is determined as follows:
Coupon rate 3 Face Value 3 (D/365)
where:
D 5 number of days from last interest payment date to the current settlement date.
In our example, the number of days from the last interest date, 25 July to 21 September, is 58
days and the accrued interest would amount to:
10.0% 3 R100 3 58/365 5 R1.59
If we use Excel, we will see that the clean price would be R101.36 at 21 September 2018 and we
add the accrued interest of R1.59 to get to an all-in price of R102.95. Sharenet was quoting an
all-in price of R102.891.
5 VALUATION OF PREFERENCE SHARES
Debenture holders (bondholders) receive a fixed interest payment each period. Preference
shareholders receive, in most cases, a fixed dividend payment. However, the company is not
obliged to pay a dividend and dividends are payable only after all expenses, including interest,
have been paid. As dividends involve a higher level of risk, investors expect to receive a
higher return. However, whilst interest is fully taxable, dividends were tax-free in the hands of
investors until 31 March 2012, and so investors who were concerned primarily with after-tax
income, required a lower pre-tax yield from preference shares. For example, a debenture with
an interest rate of 10% yielded the holder an after-tax return of 7.2% at a tax rate of 28%.
If the investor’s marginal tax rate is 40%, then this would result in an after-tax return of 6%.
Firms in South Africa were issuing preference shares at about 75% to 85% of the prime rate.
The introduction of a dividend withholding tax (DWT) at 15% and subsequent increase to
20% means that preference shares have lost some of their tax advantages relative to bonds,
debentures and other debt securities. However, for investors on a high marginal tax rate,
preference shares continue to retain a tax advantage relative to debt securities. Why issue
preference shares? Firstly, companies may not be able to utilise the interest deductions owing
to accumulated losses or depreciation deductions. Secondly, companies may be acquiring
shares rather than operating assets and in terms of the Income Tax Act, the company is not
There are bond pricing and rounding conventions and so we may obtain slight differences in prices and accrued
interest. We based our required return on the SA government 5-year bond yield (R2023) and we applied a risk
spread (premium) of 1.1%. We can see that this is very close to the return that investors are expecting from the
ES23.
1
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6-9
able to deduct interest on loans employed to acquire shares2. Thirdly, RSA banks have been
willing to subscribe for preference shares issued by firms at a rate which transfers most of the
‘interest’ tax shield to the firms.
Preference shares may be cumulative or non-cumulative in terms of dividends in arrears
and they may be either redeemable or non-redeemable. Some preference shares are
convertible into ordinary shares and some are classified as participating which means that
they will participate, at a specified rate, in the profits due to the company. We will normally
assume that preference shares are cumulative.
Cumulative non-redeemable preference shares
The valuation of a preference share is the present value of an annuity received in perpetuity.
Example 6.6: Valuation of preference share
A person would like to sell 100 preference shares. The shares have an issue price of R1 each,
and carry a dividend of 10%. Similar shares available on the stock exchange yield an 8% dividend. What is the value of the preference shares?
This requires the valuation of an amount received in perpetuity. The amount is the annual
dividend which in this case amounts to 100 3 R1 3 10% = R10. The capitalisation rate
would be the required rate of return, which is given as 8%.
The present value of the shares is R10/0.08 = R125
Notice how the value depends on the future returns and not on the issue price. We see that
the above shares are worth R125 because they yield R10 per year and it would cost R125 to
buy shares which yield R10. If we bought shares for R125 we would expect to get a return
of 8%. Therefore our annual return would be R125 3 8%, which is R10. Clearly, then, our
shares which give us R10 per year, are worth R125. It has already been mentioned that preference shares have a right to the dividend after all expenses have been met. There are times
when there are insufficient cash resources available to meet the obligation to the preference
shareholders and so the dividend is not paid (the dividend is said to have been passed). If the
preference shares are cumulative, then the dividend owing for previous years has to be made
good before the company can distribute any dividends to its ordinary shareholders. In such
cases it is necessary to estimate when the arrear dividends will be received and to discount
these to the present value at the required rate of return. Similarly, if there is an expectation
that future dividends may fall into arrears, the date of receipt of those dividends must also
be estimated.
Example 6.7: Cumulative preference share dividends in arrear
You own 100 preference shares with an issue price of R1 each in a company that has just
paid the preference dividend and has made an announcement that financially difficult times
are ahead. It is expected that the dividend for the next two years will be passed; thereafter
normal dividend payments are expected to be resumed. The preference dividend is 12%
and the required return is 14%.
The dividend for years one and two (R100 3 12% 3 2 = R24) will be received only at
the end of year three, while the dividend for year three (R12) and thereafter will be received
on schedule. One way of dealing with this is to carry out the valuation at the end of year
three and discount that value back to the present. The value at the end of year three is the
dividend which will be received on that date (arrear dividend for years one and two and the
dividend for year three) plus the value of the perpetuity.
In Chapter 17 we explain how in certain situations a company may be able to deduct interest on the acquisition
of shares.
2
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Value of dividend received in year three = R36.00
Value of perpetuity in year three = R12/0.14 = R85.71
Value of preference shares at end of year three = R121.71
Discounted back to the present, using Table C at 14% at the end of three years, the value
of the 100 preference shares is:
R121.71 3 0.6750 = R82.15 per share
Non-cumulative preference shares
Non-cumulative preference shares simply involve the valuation of the preference dividend.
An additional point to consider is whether the dividend is likely to be passed in the future
or not. If there is any probability that the dividend will be passed, the preference shares will
be worth less, since there will be no cash flow in certain years.
Example 6.8: Non-cumulative preference share dividend passed
Assume the same details as in Example 6.7 except that the preference shares are noncumulative. In this case the dividend passed for years one and two will not be received at
all – instead we have only the perpetuity starting in year three.
Value of perpetuity at the end of year 3 = ____
​ R12 ​ 5 R85.71
0.14
The value of the perpetuity in year three plus the dividend received in year three can be
discounted back to the present, using Table C at 14% at the end of three years. The value of
the preference shares is R65.95 [(R85.71 + 12.00) 3 0.675].
Redeemable preference shares
The valuation of redeemable preference shares is similar to the valuation of redeemable
debentures, which was illustrated in Example 6.5. A problem in valuing redeemable
preference shares, however, is that there will be instances when they may be redeemable
only at the option of the company. In carrying out such a valuation it is necessary to assess
the likelihood of redemption on a particular date. If the coupon interest rate is higher than
the current market interest rate, then the likelihood is that redemption will take place.
6 VALUATION OF ORDINARY EQUITY
The valuation of ordinary shares is more difficult than valuing bonds or preference shares
for the following reasons:
■■ Future cash flows are uncertain as earnings and dividends are dependent on such factors
as the state of the economy, currency rates, operating costs, interest rates, product
acceptance and the level of competition in the sector.
■■ Ordinary shares have no maturity and companies are assumed to have an indefinite life.
■■ The cost of equity and the cost of capital are subject to greater uncertainty and more
difficult to observe than bond yields.
However, the principles remain constant. The valuation of a company remains – the present
value of future cash flows. It is just more challenging to determine what the future will bring
in terms of cash flows and the discount rate.
The future cash flows that will accrue to ordinary shareholders are dividends. Changing
expectations about the growth of future dividends can have a significant impact on the value
of a company. We can also use earnings or free cash flows to value a company’s equity as
there should be a close relationship between earnings, cash flows and future dividends.
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There are various methods available to determine the value of ordinary equity:
■■ Dividend Discount Model. The value of ordinary equity is determined by the present
value of future dividends. This is also called the dividend growth model due to the effect
of growth in dividends on value.
■■ Price Multiples (relative valuation). The value of ordinary equity is determined by
using price multiples such as the price–earnings ratio or the market to book ratio.
■■ Free Cash Flow Model. We determine the free cash flows to the firm and discount this
at the firm’s cost of capital. The result is the value of the firm. We deduct the value of
debt from the value of the firm to arrive at the value of the ordinary equity. We can also
discount the equity cash flows at the cost of equity.
■■ EVA Discount Model. This requires that we discount a firm’s future EVAs at the firm’s cost of
capital. EVA was explained in Chapters 1 and 5.
Increasingly, price multiples are being referred to as the market approach to valuations and
discounted cash flow models, including the dividend discount model, are being referred to as
the income approach to valuations.
Dividend discount model
The dividend discount model requires that we project the future dividends of the firm and
discount the dividends at the firm’s cost of equity. As the firm has an indefinite life, and we
can expect earnings and dividends to grow over time, the computation of value is facilitated
if we assume a constant growth rate in dividends. Companies will normally only pay out a
percentage of earnings and the balance is reinvested to generate increased earnings and
dividends in future years. This model is also known as the dividend growth model. We will
firstly assume that dividends will grow at a constant growth rate.
Constant growth in dividends
How do we determine the value of equity if dividends are expected to grow at a constant
rate? The assumption of constant growth rate means we can use the formula of a growing
perpetuity to determine the value of equity. Firstly, we will analyse how the dividend constant growth model is derived.
The dividend growth model is based on the present value formula which is described as:
Cn 2 1
Cn
C
C2
Present Value = _____
​  1 ​ 1 ​ _______
​ 1 ............. ​​ _________
​ 1 _______
​
​
1 1 r (1 1 r)2
(1 1 r)n 2 1 (1 1 r)n
(Formula 6.2)
where: C = cash flow (expected dividend) per period
r = discount rate
Where the cash flow is growing at a constant rate, the above formula may be restated as:
C
Present Value = _____
​ r 21 g ​(Formula 6.3)
In the case of ordinary equity, the periodic cash flow is the dividend received, and so the
above model can be used as a valuation model. It is normally stated as follows:
D1
​(Formula 6.4)
Po = ​ _____
k2g
where: Po = value of ordinary share
D1 = next period’s dividend [D1 = Do(1 + g)]
k = cost of equity
g = growth rate in future dividends
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If we refer to Chapter 2, we are really valuing a growing perpetuity. If we assume that there
will be no growth in dividends, then we are valuing a perpetuity and the present value of
dividends will be determined by D1/k.
How does this formula work? Does the growth formula ignore future prices? In fact we can
show how the formula is derived by including future prices:
Po =
D1 1 P1
​ _______
​
11k
However, the value in a year’s time, P1, will also be determined by the future dividend in
year 2 and the price at the end of Year 2:
P1 =
D2 1 P2
​ _______
​
11k
If we substitute P1 into the formula above:
D2 1 P2
D1
_______
_____
Po = ​  1 1 k ​ 1 ​  (1 1 k)2 ​
Similarly, the value at Year 2 will be determined by the present value of the dividend to be
received in Year 3 and the present value of the price at the end of Year 3. Therefore the
value becomes:
D1
D2
Po = ​ _____
​
​ 1 ​ _______
11k
(1 1 k)2
1
D3 1 P3
​ _______
​
(1 1 k)3
We can continue this to infinity so that the value of the share is:
D1
D3
Dn 2 1
D2
Po = ​ _____
​ 1 ​ _______
​​ 1 ........ ​ __________
​
​ 1 ​ _______
2
3
11k
(1 1 k)
(1 1 k)
(1 1 k)n 2 1
1
Dn
Pn
________
​
​ 1 ​ ________
​
n
(1 1 k)
(1 1 k)n
The last expression is the price of the share at time infinity which discounted back to its
present value approaches zero. We are therefore left with the present value of the stream
of future dividends to infinity, which under the assumption of constant growth, reduces to
Formula 6.4. Sometimes we want to know the implicit constant growth rate in the share
price of a company. Is the assumption of future growth reasonable?
Formula 6.4 can be restated as follows to determine the implicit growth rate:
kP 2 Do
g = ________
​  o
​(Formula 6.5)
Po 1 Do
How do we value shares if investors are selling in a few years’ time?
Let’s come back to the issue of selling shares. What if an investor is planning to sell the
share in a few years’ time? Sometimes investors, particularly during the boom in technology
stocks, indicated that future dividends were not relevant, as they were planning to sell the
shares after a few years and were focused on capital gains. Often there were no dividends,
only the promise of future earnings and dividends. The market correction has changed this
philosophy and current dividends have become more highly valued. However, coming back
to our first point, if an investor is planning to hold a particular share for only three years,
then the valuation formula becomes:
D1
Po = ​ _____
​
11k
1
D2
________
​
​1
(1 1 k)2
D3 1 P3
​  ________
​
(1 1 k)3
Although the value to the investor today is affected by the value of the share in Year 3, the
future rational investor buying the share will pay a price that is determined by the future
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6-13
dividends from Year 4 onwards. Remember, the future investor is buying a stream of future
dividends. During the initial period, the company may experience an improvement in
sales or operating margins which is expected to increase future dividends. Expectations of
future dividends may change dramatically and suddenly values will change. Yet the value of
the ordinary equity will remain anchored to the principle of discounted future dividends.
Although investors may bet on events that will significantly impact on future dividend
expectations, these events may or may not happen.
If we apply the constant growth dividend model, we need to determine the following 3
variables:
■■ The next year’s dividend [current dividend 3 (1 + growth rate)];
■■ The discount rate (i.e. the cost of equity); and
■■ The growth rate in future dividends.
The next year’s dividend will be reasonably easy to forecast, by taking into account the
current year’s dividend. We simply need to take the current dividend and apply the constant
growth rate to obtain next year’s dividend per share.
The discount rate is the cost of equity, which is the return that investors require from the
investment, given the level of risk. This is discussed in greater detail in Chapter 7.
The growth rate is more difficult to estimate. Dividends are a function of policy as well
as the prevailing economic environment. The growth rate in dividends is often difficult to
determine and the assumption of a constant growth rate may not be realistic. The dividend
discount model is more relevant when we are valuing a firm with steady earnings growth
operating in a mature industry sector. The assumption of a real growth rate which is similar
to the expected real GDP growth rate plus the expected inflation rate may be relevant for
many companies operating in certain sectors. We can also make further adjustments for
productivity improvements.
What is the role of future earnings?
If one views the dividends paid by a company over the long term, then the effect of dividend
policy will tend to be smoothed out over time and the growth in dividend will more closely
reflect the growth in earnings generated by the company. Consequently, in trying to make
an estimate of growth in future dividends, it is often better to estimate the growth in future
earnings. Future earnings are not the only possible surrogate – they are merely suggested
as being potentially suitable. Growth in cash flow may well be better, or, depending on the
particular company, it may be some item even further removed from the actual dividend,
such as sales. Which surrogate is best will depend on which item most closely reflects future
dividend growth. It is suggested that expected growth in earnings and cash flow are likely to
be good surrogates for expected growth in dividends for many companies.
If dividends are affected by the growth in earnings per share and operating cash flow, then
it is important to evaluate the factors that will impact on the growth in earnings and operating
cash flow. Firstly, inflation will result in a growth in earnings per share. Even if the firm is
unable to grow in real terms, inflationary growth will result in an increase in future dividends.
Secondly, the reinvestment of earnings should result in an increase in future earnings and
dividends.
Is it possible to increase the value of a company’s shares by increasing dividends?
No, life is not that simple. Increasing next year’s dividend will increase D1 in our valuation
formula but may reduce future growth in dividends. If a company pays a higher dividend,
it means the company is reinvesting less, which will tend to reduce the future growth rate
in dividends. In most cases, higher dividends will increase equity values if the increase in
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FINANCIAL MANAGEMENT
dividends is supported by earnings growth. If a company’s earnings per share is growing by
less than its dividend per share, then the growth rate in dividends is not sustainable unless
earnings growth accelerates. On the other hand, the reinvestment of earnings and maintaining a high dividend cover will increase the value of the equity only if the company’s return
on capital is greater than the company’s cost of capital. Otherwise, growth could actually
result in the destruction of value.
The sustainable growth rate which is covered in Chapter 5 may be used as a reasonability
check as the model takes into account the return generated on assets, the degree of financial
leverage and the percentage of earnings reinvested. The model was designed to calculate
the growth in equity which should in turn reflect the potential growth in dividends.
Example 6.9: Valuation using the dividend growth model
Company X reported profits of R250m in the most recent year and has a dividend cover of
two. The industry in which it operates is in the mature phase of its development. The company expects to grow at the GDP growth rate of 3% per year. The required rate of return
in that industry is 10%.
Applying the dividend growth model:
D1
Po = ​ _____
​
k2g
Earnings are R250m and dividend policy is to have a cover of two times, so the dividend is:
R250m/2 = R125m
The other variables needed for the formula are given; growth is 3% and the required return
is 10%. The value of the company is:
R125m(1 + 0.03)/(0.10 – 0.03) = R1 839.3m
Limitations
The model is limited in the following respects:
■■ It assumes that growth is constant.
■■ It is applicable only where the required return is higher than the growth rate. As growth
approaches the required rate of return, so the value of the shares approaches infinity.
This is not likely to be a realistic valuation as it is highly improbable that a company
would be able to maintain this level of growth indefinitely.
■■ If growth exceeds the required rate of return, the model gives a negative valuation to
the shares, which is clearly absurd.
However, we can make adjustments to avoid the above limitations such as estimating future
dividends for a specific period and use the constant growth formula only once we reach a
steady state of growth.
Zero growth in dividends
If dividends are expected to remain at a fixed level, then the value of the equity is simply
the present value of a perpetuity and may be valued as follows:
Value = D1/k
If a company is expected to pay a dividend of R0.80 per share indefinitely, then the value
per ordinary share, if the cost of equity is 11% is:
Value = 0.80/0.11 = R7.27
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Let’s go back to Example 6.9 but now assume that dividends are not expected to grow and will
remain at a constant level of R125m per year. How would this change the valuation of the company?
Value = R125m/0.10 = R1 250m
This is much lower than the value we determined then of R1 839m. Even a low growth rate of
3% per year adds about R589m [1 839m – 1 250m] to our valuation. Of course, the assumption
here is that the dividend will remain initially at R125m. If we are not growing, we may be able to
afford to pay a higher dividend per year and this would increase the value of the ordinary shares.
Valuing shares with a non-constant growth rate
How do we value companies that are growing at a faster rate than the general economy and
this rate of growth is expected to last for a few years? How do we value a company that is
growing at a higher rate than the firm’s cost of capital, a relationship which is patently not
sustainable? There are also business cycles and we need to look through the cycles to estimate
the long-term growth rate in earnings and dividends.
What is a normal cycle for a firm to follow? Companies which are starting up tend
to experience high growth rates in earnings and tend to reinvest their earnings to take
advantage of high returns on capital. As competitors move into the sector or the company
becomes the dominant market player, growth in earnings tends to slow. The company will
reduce the rate of investment and as the cash starts piling up, the company is eventually
forced to use the funds to pay dividends. After a few years, dividend growth should be in
line with earnings growth.
A few observations about dividends, earnings and growth are worth noting. Dividends
and earnings must grow at the same rate over the long term. If dividends grow at a slower
rate than earnings, the dividend yield will tend towards zero, which is not feasible in the long
term as the investor will want to get the money out of the company.
A dividend growth that is greater than the earnings growth is not sustainable. This is
intuitively obvious. It can also be shown by the sustainable growth formula. An abbreviated
version of the SGR formula is: SGR = Return on equity 3 Retention ratio. But if dividends
grow at a faster rate than earnings the retention ratio will eventually become negative,
consequently the SGR is negative which is not credible. Dividends (or earnings) cannot grow
at a faster rate than the economy indefinitely. However there can be a finite period of high
growth. Consider a typical product life cycle. The product starts off slowly, it then enters the
growth phase, this growth phase slows down as the product approaches maturity, a plateau
period is reached, and then there is the decline and eventually the demise of the product.
These phases can be extended or shortened according to the strategies of management, but
nonetheless, to a greater or lesser extent, all products follow a similar pattern.
In the earlier growth phase one tends to find that the growth is faster than normal. As
competitors enter the market the growth rate will slow down and, as the market starts to
become saturated, the product reaches its plateau period. The question is whether the model
can cope with this type of situation. Indeed it can. There are two stages to the calculation:
value the high growth period and value the constant growth in dividends thereafter. This is
illustrated in Example 6.10.
Example 6.10: Two-stage valuation
High-Fly Limited is a young company in the electronic games sector. It has an appealing
new product which is expected to capture the market. It is estimated that it will be three
years before competitors are able to enter this market. High-Fly has just paid a dividend of
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60 cents per share. The required return for the sector is estimated to be 12% per annum.
Growth for the next three years is expected to be in the region of 30% and thereafter it is
expected to be the normal growth for the industry which is 6% per annum. To value the
shares of High-Fly one needs to follow the two stages mentioned above.
Stage 1: Calculate present value of dividend until the growth rate changes.
Dividend Year 1 R0.60 3 1.30 = R0.78
Dividend Year 2 R0.78 3 1.30 = R1.01
Dividend Year 3 R1.01 3 1.30 = R1.31
These dividends are discounted at 12% to arrive at the present value of R2.43 per share.
Stage 2: Value the growth on the date the growth rate changes.
The formula needs to be adapted very slightly as we are valuing the shares in year three
using the dividend stream expected from year four. Thus the formula will be:
V3 = D4/(k – g)
We know k to be 12% and g, after year three, will be 6%. The dividend will be the dividend
received in year three increased by 6%:
R1.31 3 1.06 = R1.39
Applying the formula:
R1.39/(0.12 – 0.06) = R23.17
The value in year three of the future stream of dividends is R23.17. This must be discounted
to its present value.
R23.17 3 0.7118 = R16.49
The value of a share in High-Fly3 is:
R2.43 + R16.49 = R18.92
If more than two distinct growth periods are expected, this approach can be adapted to a
three-stage or n stage model. To value the high growth period we must estimate the duration of the high growth period and the size of the dividend during this period. High returns
We have rounded off the PV factors to 4 decimal places and future dividends to 2 decimal places. Using actual
values, and a financial calculator or Excel, we will determine a more accurate value of R19.02.
3
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attract competitors into the market; therefore the difficulty of entering the market affects
the length of the period for which high returns can be sustained. Barriers to entry include
patents, trademarks, brands and company size and control over the distribution network,
amongst others. The size of the dividend is determined by the expected earnings, capital
requirements, and the dividend payout policy.
What other cycles are important? For example, a company could be operating in the mining
sector which is subject to commodity price cycles. Furthermore, declining reserves could
mean falling revenues and a terminal life for the company. We need to take into account
industry and company information in forecasting future dividend payments.
Valuing shares which do not pay dividends for many years
Let’s take an example of a biotech company that is developing a new drug. Perhaps, the
company will operate with losses for the first seven years before making a profit and may
only start paying a dividend after 10 years. For example, assume the company will start
paying a dividend of R0.20 per share in Year 11 which is expected to double in Year 12 and
again in Year 13. Assume that thereafter the dividend will grow at 7.5% per year. The cost
of equity is 14% as the company is perceived to be high risk. The value of the shares today
would be R2.69, calculated as follows:
The values of shares in companies with distant dividend cash flows are very sensitive to
changes in expectations of dividends and/or risk. For example, if the risk of the company
falls due to a successful Phase III clinical trial, or if interest rates fall and the cost of equity
is now 11%, then the value today will rise from R2.69 to R6.71.
FROM THE REAL WORLD … WOOLWORTHS
Let’s apply the dividend growth model to Woolworths, which is a major retailer in South Africa,
but also operates in Australia under the brands of David Jones and Country Road. Until 2015,
management had been very successful in increasing the company’s share price and the company
had been able to record increases in earnings and dividends. This changed dramatically and the
share price has declined from around R100 per share in late 2015 to R51 in September 2018.
This is mostly due to operating challenges in Australia. The company also got it wrong in terms
of its fashion business in 2018. Furthermore, the company operates in the retail sector which
is mature and Shoprite, Edcon, Foschini, Truworths and Pick n Pay are major competitors and
there are new competitors such as H&M and Zara.
The cost of equity of Woolworths should be around 14.0%, if we use a simple calculation of
a risk-free rate of 9% plus a risk premium of 5%. The growth in the retail market should reflect
underlying growth in GDP. Economic growth is currently low but we have estimated real growth
of 3% per year and inflation of about 5%. This means we will use a sustainable constant growth
rate of 8%. If we compare the dividends and earnings per share of Woolworths in recent years,
we see the following pattern:
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The growth in earnings per share (EPS) from 2012 to 2018 has been 7.8% [(3.463/2.051)1/7 – 1]
per year and the growth in dividend per share (DPS) has been 8.3% [(2.39/1.37)1/7 – 1] per year.
This is a reasonable growth rate, although growth over the last two years has been negative.
There is uncertainty over the group’s transformational initiatives in Australia, but Woolworths
should be able to ensure a recovery of margins from its fashion business in 2019. Operating
profit fell by 15% in 2018, after an 11% fall in 2017. We will assume that Woolworths will grow
by 15% in 2019 in order to get back to 2017 levels. Thereafter, we have assumed a steady increase
in earnings of 11% per year over the period 2019 to 2023. Thereafter, we have assumed that
Woolworths will be able to achieve a sustainable growth rate of 8% per year. The expected
dividend for 2019 is therefore R2.7485 (2.39  1.15). The value per share is expected to be close
to R50.44.
The valuation is sensitive to changes in interest rates and changes to the required return (cost of
equity). If we increase the cost of equity to 15%, our value falls from R50.44 to R43. If we reduce
the cost of equity to 13%, the current value increases to R61.
The share price on 21 September 2018 was R51. This is very close to the above valuation
and we consider that any turnaround has been mostly factored into the current share price. In
our view investors are expecting Woolworths to get it right but we consider that there is some
risk that the transformational initiatives in Australia may not be successful and so earnings may
continue to be under pressure for a few years. However, the company retains an option to reduce
its presence in Australia if things do not work out, although this may be constrained by its leases.
In the long term, Woolworths will always be a leading retailer in South Africa, which will provide
support to its share price.
Price multiples (relative valuation)
Whilst the dividend discount model and the free cash flow model are both based on discounting future cash flows, investors also use price multiples such as the price–earnings
(P/E) ratio and the price to book value ratio to determine whether shares are over or
under-valued.
The price–earnings (P/E) ratio
The P/E ratio measures the relationship between the company’s earnings per share and
the share price. If a company’s share price is currently trading at R15 and the earnings per
share is R1.25, then the company is on a P/E ratio of 12 (15/1.25). Investors are prepared
to pay 12 times the firm’s earnings per share.
How do we use P/E ratios to value companies? We need to find out the P/E ratios of
comparable companies or the sector’s average P/E ratio. For example, assume that we are
valuing a company in the food and drug retailers sector which is trading at a P/E ratio of 12.
The sector average is 17 and therefore this may indicate that the company is undervalued,
but there could be other valid reasons for the difference in P/E ratios.
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The value of the company based on the industry sector average P/E would be:
Value = EPS  P/E = 1.25  17 = R21.25
We would therefore buy the share as the current price is R15.
Companies experiencing high growth rates in earnings will normally have high P/E ratios
whilst companies with a high level of financial leverage may have lower P/E ratios, to reflect
the higher risk profi